%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO370^5 : 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 09:54:04 AM UTC 2026
% Result : Theorem 1.47s 1.28s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 10 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 43 ( 6 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 44 ( 17 ~; 0 |; 0 &; 20 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 2 con; 0-2 aty)
% Number of variables : 6 ( 6 ^; 0 !; 0 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cA: $i > $o ).
thf(func_def_1,type,
cP: ( $i > $o ) > $o ).
thf(f11,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f10]) ).
thf(f10,plain,
$true = $false,
inference(boolean_simplification,[status(thm)],[f9]) ).
thf(f9,plain,
( ( ~ $true ) = $true ),
inference(boolean_simplification,[status(thm)],[f8]) ).
thf(f8,plain,
( $true
= ( ~ ( ( cP @ cA )
=> ( cP @ cA ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ~ ( ( cP @ cA )
=> ( cP
@ ^ [Y0: $i] : ( cA @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ~ ( ( cP @ cA )
=> ( cP
@ ^ [Y0: $i] :
~ ~ ( cA @ Y0 ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ~ ( ( cP @ cA )
=> ( cP
@ ^ [Y0: $i] :
~ ~ ( cA @ Y0 ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( cP @ cA )
=> ( cP
@ ^ [X0: $i] :
~ ~ ( cA @ X0 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( cP @ cA )
=> ( cP
@ ^ [X0: $i] :
~ ~ ( cA @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( cP @ cA )
=> ( cP
@ ^ [X0: $i] :
~ ~ ( cA @ X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.NbzttTcY8z/DTF2THF_2555.p',cTRIVEXT3) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO370^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n022.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 14:28:51 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
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : SYO370^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.47 % Domain : Syntactic
% 0.28/0.47 % Problem : TPS problem from EXTENSIONALITY
% 0.28/0.47 % Version : Especial.
% 0.28/0.47 % English :
% 0.28/0.47
% 0.28/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.47 % Source : [Bro09]
% 0.28/0.47 % Names : tps_0643 [Bro09]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 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 v6.2.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v5.3.0, 0.25 v4.1.0, 0.33 v4.0.0
% 0.28/0.47 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.28/0.47 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 4 ( 4 avg)
% 0.28/0.47 % Number of connectives : 6 ( 2 ~; 0 |; 0 &; 3 @)
% 0.28/0.47 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 7 ( 7 avg)
% 0.28/0.47 % Number of types : 2 ( 0 usr)
% 0.28/0.47 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 2 ( 2 usr; 0 con; 1-1 aty)
% 0.28/0.47 % Number of variables : 1 ( 1 ^; 0 !; 0 ?; 1 :)
% 0.28/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.28/0.47
% 0.28/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.28/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.28/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.28/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 thf(cA,type,
% 0.28/0.47 cA: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(cP,type,
% 0.28/0.47 cP: ( $i > $o ) > $o ).
% 0.28/0.47
% 0.28/0.47 thf(cTRIVEXT3,conjecture,
% 0.28/0.47 ( ( cP @ cA )
% 0.28/0.47 => ( cP
% 0.28/0.47 @ ^ [Xx: $i] :
% 0.28/0.47 ~ ~ ( cA @ Xx ) ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 1.47/1.25 ---- Embedded in THF ---
% 1.47/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.25 %%% Generated on Tue Feb 24 14:28:52 EST 2026
% 1.47/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.25 %%% Logic specification used:
% 1.47/1.25 %%% thf(spec, logic, $$dhol).
% 1.47/1.25
% 1.47/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.NbzttTcY8z/DTF2DTF2555.p
% See solution above
% 1.47/1.25 ------------------------
% 1.47/1.26 ---- Cleaned THF ---
% 1.47/1.26 thf(cA,type,
% 1.47/1.26 cA: $i > $o ).
% 1.47/1.26
% 1.47/1.26 thf(cP,type,
% 1.47/1.26 cP: ( $i > $o ) > $o ).
% 1.47/1.26
% 1.47/1.26 thf(cTRIVEXT3,conjecture,
% 1.47/1.26 ( ( cP @ cA )
% 1.47/1.26 => ( cP
% 1.47/1.26 @ ^ [Xx: $i] :
% 1.47/1.26 ~ ~ ( cA @ Xx ) ) ) ).
% 1.47/1.26 ------------------------
% 1.47/1.27 % (2776)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_2555 for (3000ds/2Mi)
% 1.47/1.27 % (2776)First to succeed.
% 1.47/1.28 % (2776)Refutation found. Thanks to Tanya!
% 1.47/1.28 % SZS status Theorem for DTF2THF_2555
% 1.47/1.28 % SZS output start Proof for DTF2THF_2555
% 1.47/1.28 thf(func_def_0, type, cA: $i > $o).
% 1.47/1.28 thf(func_def_1, type, cP: ($i > $o) > $o).
% 1.47/1.28 thf(f11,plain,(
% 1.47/1.28 $false),
% 1.47/1.28 inference(trivial_inequality_removal,[status(thm)],[f10])).
% 1.47/1.28 thf(f10,plain,(
% 1.47/1.28 ($true = $false)),
% 1.47/1.28 inference(boolean_simplification,[status(thm)],[f9])).
% 1.47/1.28 thf(f9,plain,(
% 1.47/1.28 ((~ $true) = $true)),
% 1.47/1.28 inference(boolean_simplification,[status(thm)],[f8])).
% 1.47/1.28 thf(f8,plain,(
% 1.47/1.28 ($true = (~ ((cP @ cA) => (cP @ cA))))),
% 1.47/1.28 inference(beta_eta_normalization,[status(thm)],[f7])).
% 1.47/1.28 thf(f7,plain,(
% 1.47/1.28 ((~ ((cP @ cA) => (cP @ (^[Y0 : $i]: (cA @ Y0))))) = $true)),
% 1.47/1.28 inference(boolean_simplification,[status(thm)],[f6])).
% 1.47/1.28 thf(f6,plain,(
% 1.47/1.28 ((~ ((cP @ cA) => (cP @ (^[Y0 : $i]: (~ (~ (cA @ Y0))))))) = $true)),
% 1.47/1.28 inference(cnf_transformation,[status(thm)],[f5])).
% 1.47/1.28 thf(f5,plain,(
% 1.47/1.28 ((~ ((cP @ cA) => (cP @ (^[Y0 : $i]: (~ (~ (cA @ Y0))))))) = $true)),
% 1.47/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.47/1.28 thf(f4,plain,(
% 1.47/1.28 ~((cP @ cA) => (cP @ (^[X0 : $i] : (~~(cA @ X0)))))),
% 1.47/1.28 inference(rectify,[status(thm)],[f2])).
% 1.47/1.28 thf(f2,negated_conjecture,(
% 1.47/1.28 ~((cP @ cA) => (cP @ (^[X0 : $i] : (~~(cA @ X0)))))),
% 1.47/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.47/1.28 thf(f1,conjecture,(
% 1.47/1.28 (cP @ cA) => (cP @ (^[X0 : $i] : (~~(cA @ X0))))),
% 1.47/1.28 file('/export/starexec/sandbox2/tmp/tmp.NbzttTcY8z/DTF2THF_2555.p',cTRIVEXT3)).
% 1.47/1.28 % SZS output end Proof for DTF2THF_2555
% 1.47/1.28 % (2776)------------------------------
% 1.47/1.28 % (2776)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.28 % (2776)Termination reason: Refutation
% 1.47/1.28
% 1.47/1.28 % (2776)Memory used [KB]: 5373
% 1.47/1.28 % (2776)Time elapsed: 0.002 s
% 1.47/1.28 % (2776)------------------------------
% 1.47/1.28 % (2776)------------------------------
% 1.47/1.28 % (2771)Success in time 0.011 s
%------------------------------------------------------------------------------