%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV012^5 : 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 : n005.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 09:40:03 AM UTC 2026
% Result : Theorem 1.34s 1.20s
% Output : Refutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 8 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 42 ( 7 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 26 ( 6 ~; 0 |; 12 &; 0 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 3 ( 0 usr; 2 con; 0-2 aty)
% Number of variables : 38 ( 28 ^; 10 !; 0 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(f9,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: $o,Y1: $o] : $true )
!= ( ^ [Y0: $o,Y1: $o] : $true ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [Y0: $o,Y1: $o] : $true )
!= ( ^ [Y0: $o,Y1: $o] : $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ^ [Y0: $o,Y1: $o] : $true )
!= ( ^ [Y0: $o,Y1: $o] : $true ) ),
inference(true_and_false_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( $true
=> $true )
& ( ( ^ [Y0: $o,Y1: $o] : $true )
= ( ^ [Y0: $o,Y1: $o] : $true ) )
& ( ( $true
& $true )
=> $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( $true
=> $true )
& ( ( ^ [X2: $o,X3: $o] : $true )
= ( ^ [X4: $o,X5: $o] : $true ) )
& ( ( $true
& $true )
=> $true ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X1: $o,X0: $o] :
( $true
=> $true )
& ( ( ^ [X0: $o,X1: $o] : $true )
= ( ^ [X0: $o,X1: $o] : $true ) )
& ! [X1: $o,X2: $o,X0: $o] :
( ( $true
& $true )
=> $true ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X1: $o,X0: $o] :
( $true
=> $true )
& ( ( ^ [X0: $o,X1: $o] : $true )
= ( ^ [X0: $o,X1: $o] : $true ) )
& ! [X1: $o,X2: $o,X0: $o] :
( ( $true
& $true )
=> $true ) ),
file('/export/starexec/sandbox/tmp/tmp.MheCXI9a8Y/DTF2THF_6598.p',cTHM519_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV012^5 : 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
% 0.13/0.31 % Computer : n005.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 300
% 0.13/0.31 % DateTime : Tue Feb 24 12:38:14 EST 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/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 : SEV012^5 : TPTP v9.2.1. Released v4.0.0.
% 0.15/0.41 % Domain : Set Theory (Relations)
% 0.15/0.41 % Problem : TPS problem from EQUIVALENCE-RELATIONS-THMS
% 0.15/0.41 % Version : Especial.
% 0.15/0.41 % English :
% 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_0854 [Bro09]
% 0.15/0.41
% 0.15/0.41 % Status : Theorem
% 0.15/0.41 % Rating : 0.00 v6.2.0, 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 : 1 ( 0 unt; 0 typ; 0 def)
% 0.15/0.41 % Number of atoms : 8 ( 1 equ; 0 cnn)
% 0.15/0.41 % Maximal formula atoms : 6 ( 8 avg)
% 0.15/0.41 % Number of connectives : 5 ( 0 ~; 0 |; 3 &; 0 @)
% 0.15/0.41 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.15/0.41 % Maximal formula depth : 8 ( 8 avg)
% 0.15/0.41 % Number of types : 1 ( 0 usr)
% 0.15/0.41 % Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 0.15/0.41 % Number of symbols : 2 ( 0 usr; 1 con; 0-2 aty)
% 0.15/0.41 % Number of variables : 9 ( 4 ^; 5 !; 0 ?; 9 :)
% 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 %------------------------------------------------------------------------------
% 0.15/0.41 thf(cTHM519_pme,conjecture,
% 0.15/0.41 ( ! [Xx: $o,Xy: $o] :
% 0.15/0.41 ( $true
% 0.15/0.41 => $true )
% 0.15/0.41 & ! [Xx: $o,Xy: $o,Xz: $o] :
% 0.15/0.41 ( ( $true
% 0.15/0.41 & $true )
% 0.15/0.41 => $true )
% 0.15/0.41 & ( ( ^ [Xx: $o,Xy: $o] : $true )
% 0.15/0.41 = ( ^ [Xx: $o,Xy: $o] : $true ) ) ) ).
% 0.15/0.41
% 0.15/0.41 %------------------------------------------------------------------------------
% 0.15/0.41 ------------------------
% 1.21/1.17 ---- Embedded in THF ---
% 1.21/1.17 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.21/1.17 %%% Generated on Tue Feb 24 12:38:15 EST 2026
% 1.21/1.17 %%% using '$$dhol' embedding, version 1.3.0.
% 1.21/1.17 %%% Logic specification used:
% 1.21/1.17 %%% thf(spec, logic, $$dhol).
% 1.21/1.17
% 1.21/1.17 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.MheCXI9a8Y/DTF2DTF6598.p
% See solution above
% 1.21/1.17 ------------------------
% 1.21/1.18 ---- Cleaned THF ---
% 1.21/1.19 thf(cTHM519_pme,conjecture,
% 1.21/1.19 ( ! [Xx: $o,Xy: $o] :
% 1.21/1.19 ( $true
% 1.21/1.19 => $true )
% 1.21/1.19 & ! [Xx: $o,Xy: $o,Xz: $o] :
% 1.21/1.19 ( ( $true
% 1.21/1.19 & $true )
% 1.21/1.19 => $true )
% 1.21/1.19 & ( ( ^ [Xx: $o,Xy: $o] : $true )
% 1.21/1.19 = ( ^ [Xx: $o,Xy: $o] : $true ) ) ) ).
% 1.21/1.19 ------------------------
% 1.34/1.20 % (6861)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_6598 for (2999ds/4Mi)
% 1.34/1.20 % (6864)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_6598 for (2999ds/2Mi)
% 1.34/1.20 % (6861)First to succeed.
% 1.34/1.20 % (6864)Also succeeded, but the first one will report.
% 1.34/1.20 % (6861)Refutation found. Thanks to Tanya!
% 1.34/1.20 % SZS status Theorem for DTF2THF_6598
% 1.34/1.20 % SZS output start Proof for DTF2THF_6598
% 1.34/1.20 thf(f9,plain,(
% 1.34/1.20 $false),
% 1.34/1.20 inference(trivial_inequality_removal,[status(thm)],[f8])).
% 1.34/1.20 thf(f8,plain,(
% 1.34/1.20 ((^[Y0 : $o]: ((^[Y1 : $o]: ($true)))) != (^[Y0 : $o]: ((^[Y1 : $o]: ($true)))))),
% 1.34/1.20 inference(cnf_transformation,[status(thm)],[f7])).
% 1.34/1.20 thf(f7,plain,(
% 1.34/1.20 ((^[Y0 : $o]: ((^[Y1 : $o]: ($true)))) != (^[Y0 : $o]: ((^[Y1 : $o]: ($true)))))),
% 1.34/1.20 inference(flattening,[status(thm)],[f6])).
% 1.34/1.20 thf(f6,plain,(
% 1.34/1.20 ~((^[Y0 : $o]: ((^[Y1 : $o]: ($true)))) = (^[Y0 : $o]: ((^[Y1 : $o]: ($true)))))),
% 1.34/1.20 inference(true_and_false_elimination,[status(thm)],[f5])).
% 1.34/1.20 thf(f5,plain,(
% 1.34/1.20 ~(($true => $true) & ((^[Y0 : $o]: ((^[Y1 : $o]: ($true)))) = (^[Y0 : $o]: ((^[Y1 : $o]: ($true))))) & (($true & $true) => $true))),
% 1.34/1.20 inference(fool_elimination,[status(thm)],[f4])).
% 1.34/1.20 thf(f4,plain,(
% 1.34/1.20 ~(($true => $true) & ((^[X2 : $o, X3 : $o] : ($true)) = (^[X4 : $o, X5 : $o] : ($true))) & (($true & $true) => $true))),
% 1.34/1.20 inference(rectify,[status(thm)],[f2])).
% 1.34/1.20 thf(f2,negated_conjecture,(
% 1.34/1.20 ~(! [X1 : $o,X0 : $o] : ($true => $true) & ((^[X0 : $o, X1 : $o] : ($true)) = (^[X0 : $o, X1 : $o] : ($true))) & ! [X1 : $o,X2 : $o,X0 : $o] : (($true & $true) => $true))),
% 1.34/1.20 inference(negated_conjecture,[status(cth)],[f1])).
% 1.34/1.20 thf(f1,conjecture,(
% 1.34/1.20 ! [X1 : $o,X0 : $o] : ($true => $true) & ((^[X0 : $o, X1 : $o] : ($true)) = (^[X0 : $o, X1 : $o] : ($true))) & ! [X1 : $o,X2 : $o,X0 : $o] : (($true & $true) => $true)),
% 1.34/1.20 file('/export/starexec/sandbox/tmp/tmp.MheCXI9a8Y/DTF2THF_6598.p',cTHM519_pme)).
% 1.34/1.20 % SZS output end Proof for DTF2THF_6598
% 1.34/1.20 % (6861)------------------------------
% 1.34/1.20 % (6861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.20 % (6861)Termination reason: Refutation
% 1.34/1.20
% 1.34/1.20 % (6861)Memory used [KB]: 5373
% 1.34/1.20 % (6861)Time elapsed: 0.002 s
% 1.34/1.20 % (6861)Instructions burned: 1 (million)
% 1.34/1.20 % (6861)------------------------------
% 1.34/1.20 % (6861)------------------------------
% 1.34/1.20 % (6857)Success in time 0.012 s
%------------------------------------------------------------------------------