%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV160^5 : 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 : n022.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 1.07s 1.10s
% Output : Refutation 1.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 1
% Syntax : Number of formulae : 7 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 7 ( 6 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 29 ( 5 ~; 0 |; 0 &; 24 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 2 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 2 usr; 3 con; 0-2 aty)
% Number of variables : 12 ( 12 ^; 0 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
y: a ).
thf(func_def_2,type,
x: a ).
thf(f8,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [Y0: a > a > a] : ( Y0 @ x @ y ) )
!= ( ^ [Y0: a > a > a] : ( Y0 @ x @ y ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ^ [Y0: a > a > a] : ( Y0 @ x @ y ) )
!= ( ^ [Y0: a > a > a] : ( Y0 @ x @ y ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ^ [Y0: a > a > a] : ( Y0 @ x @ y ) )
!= ( ^ [Y0: a > a > a] : ( Y0 @ x @ y ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
( ( ^ [X0: a > a > a] : ( X0 @ x @ y ) )
!= ( ^ [X1: a > a > a] : ( X1 @ x @ y ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
( ( ^ [X0: a > a > a] : ( X0 @ x @ y ) )
!= ( ^ [X0: a > a > a] : ( X0 @ x @ y ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ^ [X0: a > a > a] : ( X0 @ x @ y ) )
= ( ^ [X0: a > a > a] : ( X0 @ x @ y ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.rpUpfLz8st/DTF2THF_21609.p',cTHM186_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV160^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n022.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Feb 24 12:41:06 EST 2026
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.41 ---- Original DTF file ---
% 0.15/0.41 thf(spec,logic,$$dhol).
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 % File : SEV160^5 : TPTP v9.2.1. Released v4.0.0.
% 0.15/0.41 % Domain : Set Theory
% 0.15/0.41 % Problem : TPS problem THM186
% 0.15/0.41 % Version : Especial.
% 0.15/0.41 % English : Basic theorem about pairing.
% 0.15/0.41
% 0.15/0.41 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.15/0.41 % Source : [Bro09]
% 0.15/0.41 % Names : tps_0061 [Bro09]
% 0.15/0.41 % : THM186 [TPS]
% 0.15/0.41
% 0.15/0.41 % Status : Theorem
% 0.15/0.41 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 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
% 0.15/0.41 % Syntax : Number of formulae : 4 ( 1 unt; 3 typ; 0 def)
% 0.15/0.41 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.15/0.41 % Maximal formula atoms : 1 ( 1 avg)
% 0.15/0.41 % Number of connectives : 4 ( 0 ~; 0 |; 0 &; 4 @)
% 0.15/0.41 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.15/0.41 % Maximal formula depth : 1 ( 1 avg)
% 0.15/0.41 % Number of types : 1 ( 1 usr)
% 0.15/0.41 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.15/0.41 % Number of symbols : 3 ( 2 usr; 2 con; 0-2 aty)
% 0.15/0.41 % Number of variables : 2 ( 2 ^; 0 !; 0 ?; 2 :)
% 0.15/0.41 % SPC : TH0_THM_EQU_NAR
% 0.15/0.41
% 0.15/0.41 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.15/0.41 % project in the Department of Mathematical Sciences at Carnegie
% 0.15/0.41 % Mellon University. Distributed under the Creative Commons copyleft
% 0.15/0.41 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.15/0.41 % : Polymorphic definitions expanded.
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 thf(a_type,type,
% 0.15/0.41 a: $tType ).
% 0.15/0.41
% 0.15/0.41 thf(y,type,
% 0.15/0.41 y: a ).
% 0.15/0.41
% 0.15/0.41 thf(x,type,
% 0.15/0.41 x: a ).
% 0.15/0.41
% 0.15/0.41 thf(cTHM186_pme,conjecture,
% 0.15/0.41 ( ( ^ [Xg: a > a > a] : ( Xg @ x @ y ) )
% 0.15/0.41 = ( ^ [Xg: a > a > a] : ( Xg @ x @ y ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 ------------------------
% 1.07/1.08 ---- Embedded in THF ---
% 1.07/1.08 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.07/1.08 %%% Generated on Tue Feb 24 12:41:06 EST 2026
% 1.07/1.08 %%% using '$$dhol' embedding, version 1.3.0.
% 1.07/1.08 %%% Logic specification used:
% 1.07/1.08 %%% thf(spec, logic, $$dhol).
% 1.07/1.08
% 1.07/1.08 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.rpUpfLz8st/DTF2DTF21609.p
% See solution above
% 1.07/1.08 ------------------------
% 1.07/1.09 ---- Cleaned THF ---
% 1.07/1.09 thf(a_type,type,
% 1.07/1.09 a: $tType ).
% 1.07/1.09
% 1.07/1.09 thf(y,type,
% 1.07/1.09 y: a ).
% 1.07/1.09
% 1.07/1.09 thf(x,type,
% 1.07/1.09 x: a ).
% 1.07/1.09
% 1.07/1.09 thf(cTHM186_pme,conjecture,
% 1.07/1.09 ( ( ^ [Xg: a > a > a] : ( Xg @ x @ y ) )
% 1.07/1.09 = ( ^ [Xg: a > a > a] : ( Xg @ x @ y ) ) ) ).
% 1.07/1.09 ------------------------
% 1.07/1.10 % (21770)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21609 for (3000ds/183Mi)
% 1.07/1.10 % (21776)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21609 for (3000ds/18Mi)
% 1.07/1.10 % (21773)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21609 for (3000ds/2Mi)
% 1.07/1.10 % (21775)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_21609 for (3000ds/275Mi)
% 1.07/1.10 % (21774)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_21609 for (3000ds/2Mi)
% 1.07/1.10 % (21772)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_21609 for (3000ds/27Mi)
% 1.07/1.10 % (21771)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_21609 for (3000ds/4Mi)
% 1.07/1.10 % (21775)First to succeed.
% 1.07/1.10 % (21770)Also succeeded, but the first one will report.
% 1.07/1.10 % (21774)Also succeeded, but the first one will report.
% 1.07/1.10 % (21775)Refutation found. Thanks to Tanya!
% 1.07/1.10 % SZS status Theorem for DTF2THF_21609
% 1.07/1.10 % SZS output start Proof for DTF2THF_21609
% 1.07/1.10 thf(type_def_5, type, a: $tType).
% 1.07/1.10 thf(func_def_0, type, a: $tType).
% 1.07/1.10 thf(func_def_1, type, y: a).
% 1.07/1.10 thf(func_def_2, type, x: a).
% 1.07/1.10 thf(f8,plain,(
% 1.07/1.10 $false),
% 1.07/1.10 inference(trivial_inequality_removal,[status(thm)],[f7])).
% 1.07/1.10 thf(f7,plain,(
% 1.07/1.10 ((^[Y0 : a > a > a]: (Y0 @ x @ y)) != (^[Y0 : a > a > a]: (Y0 @ x @ y)))),
% 1.07/1.10 inference(cnf_transformation,[status(thm)],[f6])).
% 1.07/1.10 thf(f6,plain,(
% 1.07/1.10 ((^[Y0 : a > a > a]: (Y0 @ x @ y)) != (^[Y0 : a > a > a]: (Y0 @ x @ y)))),
% 1.07/1.10 inference(flattening,[status(thm)],[f5])).
% 1.07/1.10 thf(f5,plain,(
% 1.07/1.10 ~((^[Y0 : a > a > a]: (Y0 @ x @ y)) = (^[Y0 : a > a > a]: (Y0 @ x @ y)))),
% 1.07/1.10 inference(fool_elimination,[status(thm)],[f4])).
% 1.07/1.10 thf(f4,plain,(
% 1.07/1.10 ~((^[X0 : a > a > a] : (X0 @ x @ y)) = (^[X1 : a > a > a] : (X1 @ x @ y)))),
% 1.07/1.10 inference(rectify,[status(thm)],[f2])).
% 1.07/1.10 thf(f2,negated_conjecture,(
% 1.07/1.10 ~((^[X0 : a > a > a] : (X0 @ x @ y)) = (^[X0 : a > a > a] : (X0 @ x @ y)))),
% 1.07/1.10 inference(negated_conjecture,[status(cth)],[f1])).
% 1.07/1.10 thf(f1,conjecture,(
% 1.07/1.10 ((^[X0 : a > a > a] : (X0 @ x @ y)) = (^[X0 : a > a > a] : (X0 @ x @ y)))),
% 1.07/1.10 file('/export/starexec/sandbox2/tmp/tmp.rpUpfLz8st/DTF2THF_21609.p',cTHM186_pme)).
% 1.07/1.10 % SZS output end Proof for DTF2THF_21609
% 1.07/1.10 % (21775)------------------------------
% 1.07/1.10 % (21775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.07/1.10 % (21775)Termination reason: Refutation
% 1.07/1.10
% 1.07/1.10 % (21775)Memory used [KB]: 5373
% 1.07/1.10 % (21775)Time elapsed: 0.002 s
% 1.07/1.10 % (21775)------------------------------
% 1.07/1.10 % (21775)------------------------------
% 1.07/1.10 % (21769)Success in time 0.011 s
%------------------------------------------------------------------------------