%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO262^5 : 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 : n001.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 09:53:47 AM UTC 2026
% Result : Theorem 1.38s 1.20s
% Output : Refutation 1.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 59 ( 10 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 153 ( 31 ~; 0 |; 6 &; 116 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 21 ^; 15 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cP: $i > $i > $o ).
thf(func_def_1,type,
cE: ( $i > $o ) > $i ).
thf(func_def_9,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f12,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f11]) ).
thf(f11,plain,
$true != $true,
inference(superposition,[status(thm)],[f8,f10]) ).
thf(f10,plain,
! [X0: $i] :
( $true
= ( cP @ X0 @ ( cE @ ( cP @ X0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i] :
( ( cP @ X0
@ ( cE
@ ^ [Y0: $i] : ( cP @ X0 @ Y0 ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X0: $i] :
( ( cP @ X0
@ ( cE
@ ^ [Y0: $i] : ( cP @ X0 @ Y0 ) ) )
= $true )
& ! [X1: $i > $i] :
( $true
!= ( cP
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0 @ ( X1 @ Y0 ) ) )
@ ( X1
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0 @ ( X1 @ Y0 ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
~ ~ ( ! [X0: $i] :
( ( cP @ X0
@ ( cE
@ ^ [Y0: $i] : ( cP @ X0 @ Y0 ) ) )
= $true )
& ! [X1: $i > $i] :
( $true
!= ( cP
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0 @ ( X1 @ Y0 ) ) )
@ ( X1
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0 @ ( X1 @ Y0 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ~ ( ! [X0: $i] :
( ( cP @ X0
@ ( cE
@ ^ [Y0: $i] : ( cP @ X0 @ Y0 ) ) )
= $true )
& ! [X2: $i > $i] :
( $true
!= ( cP
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0 @ ( X2 @ Y0 ) ) )
@ ( X2
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0 @ ( X2 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ~ ( ! [X0: $i] :
( cP @ X0
@ ( cE
@ ^ [X1: $i] : ( cP @ X0 @ X1 ) ) )
& ! [X2: $i > $i] :
~ ( cP
@ ( cE
@ ^ [X3: $i] :
~ ( cP @ X3 @ ( X2 @ X3 ) ) )
@ ( X2
@ ( cE
@ ^ [X4: $i] :
~ ( cP @ X4 @ ( X2 @ X4 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ~ ( ! [X0: $i] :
( cP @ X0
@ ( cE
@ ^ [X1: $i] : ( cP @ X0 @ X1 ) ) )
& ! [X2: $i > $i] :
~ ( cP
@ ( cE
@ ^ [X0: $i] :
~ ( cP @ X0 @ ( X2 @ X0 ) ) )
@ ( X2
@ ( cE
@ ^ [X0: $i] :
~ ( cP @ X0 @ ( X2 @ X0 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
~ ( ! [X0: $i] :
( cP @ X0
@ ( cE
@ ^ [X1: $i] : ( cP @ X0 @ X1 ) ) )
& ! [X2: $i > $i] :
~ ( cP
@ ( cE
@ ^ [X0: $i] :
~ ( cP @ X0 @ ( X2 @ X0 ) ) )
@ ( X2
@ ( cE
@ ^ [X0: $i] :
~ ( cP @ X0 @ ( X2 @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.afu61bwxoH/DTF2THF_14445.p',cTHM19SK1) ).
thf(f8,plain,
! [X1: $i > $i] :
( $true
!= ( cP
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0 @ ( X1 @ Y0 ) ) )
@ ( X1
@ ( cE
@ ^ [Y0: $i] :
~ ( cP @ Y0 @ ( X1 @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO262^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.32 % Computer : n001.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 14:27:50 EST 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.44 ---- Original DTF file ---
% 0.17/0.44 thf(spec,logic,$$dhol).
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 % File : SYO262^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.44 % Domain : Syntactic
% 0.17/0.44 % Problem : TPS problem THM19SK1
% 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_0152 [Bro09]
% 0.17/0.44 % : THM19SK1 [TPS]
% 0.17/0.44
% 0.17/0.44 % Status : Theorem
% 0.17/0.44 % Rating : 0.25 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.25 v7.4.0, 0.22 v7.3.0, 0.30 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.00 v4.0.1, 0.33 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 ( 0 equ; 0 cnn)
% 0.17/0.44 % Maximal formula atoms : 5 ( 5 avg)
% 0.17/0.44 % Number of connectives : 21 ( 4 ~; 0 |; 1 &; 16 @)
% 0.17/0.44 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.17/0.44 % Maximal formula depth : 12 ( 12 avg)
% 0.17/0.44 % Number of types : 2 ( 0 usr)
% 0.17/0.44 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.17/0.44 % Number of symbols : 2 ( 2 usr; 0 con; 1-2 aty)
% 0.17/0.44 % Number of variables : 5 ( 3 ^; 2 !; 0 ?; 5 :)
% 0.17/0.44 % SPC : TH0_THM_NEQ_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 %------------------------------------------------------------------------------
% 0.17/0.44 thf(cP,type,
% 0.17/0.44 cP: $i > $i > $o ).
% 0.17/0.44
% 0.17/0.44 thf(cE,type,
% 0.17/0.44 cE: ( $i > $o ) > $i ).
% 0.17/0.44
% 0.17/0.44 thf(cTHM19SK1,conjecture,
% 0.17/0.44 ~ ( ! [Xx: $i] :
% 0.17/0.44 ( cP @ Xx
% 0.17/0.44 @ ( cE
% 0.17/0.44 @ ^ [Xy: $i] : ( cP @ Xx @ Xy ) ) )
% 0.17/0.44 & ! [Xf: $i > $i] :
% 0.17/0.44 ~ ( cP
% 0.17/0.44 @ ( cE
% 0.17/0.44 @ ^ [Xx: $i] :
% 0.17/0.44 ~ ( cP @ Xx @ ( Xf @ Xx ) ) )
% 0.17/0.44 @ ( Xf
% 0.17/0.44 @ ( cE
% 0.17/0.44 @ ^ [Xx: $i] :
% 0.17/0.44 ~ ( cP @ Xx @ ( Xf @ Xx ) ) ) ) ) ) ).
% 0.17/0.44
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 ------------------------
% 1.26/1.17 ---- Embedded in THF ---
% 1.26/1.17 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.26/1.17 %%% Generated on Tue Feb 24 14:27:51 EST 2026
% 1.26/1.17 %%% using '$$dhol' embedding, version 1.3.0.
% 1.26/1.17 %%% Logic specification used:
% 1.26/1.17 %%% thf(spec, logic, $$dhol).
% 1.26/1.17
% 1.26/1.17 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.afu61bwxoH/DTF2DTF14445.p
% See solution above
% 1.26/1.17 ------------------------
% 1.26/1.18 ---- Cleaned THF ---
% 1.26/1.18 thf(cP,type,
% 1.26/1.18 cP: $i > $i > $o ).
% 1.26/1.18
% 1.26/1.18 thf(cE,type,
% 1.26/1.18 cE: ( $i > $o ) > $i ).
% 1.26/1.18
% 1.26/1.18 thf(cTHM19SK1,conjecture,
% 1.26/1.18 ~ ( ! [Xx: $i] :
% 1.26/1.18 ( cP @ Xx
% 1.26/1.18 @ ( cE
% 1.26/1.18 @ ^ [Xy: $i] : ( cP @ Xx @ Xy ) ) )
% 1.26/1.18 & ! [Xf: $i > $i] :
% 1.26/1.18 ~ ( cP
% 1.26/1.18 @ ( cE
% 1.26/1.18 @ ^ [Xx: $i] :
% 1.26/1.18 ~ ( cP @ Xx @ ( Xf @ Xx ) ) )
% 1.26/1.18 @ ( Xf
% 1.26/1.18 @ ( cE
% 1.26/1.18 @ ^ [Xx: $i] :
% 1.26/1.18 ~ ( cP @ Xx @ ( Xf @ Xx ) ) ) ) ) ) ).
% 1.26/1.18 ------------------------
% 1.26/1.19 % (14547)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14445 for (2999ds/183Mi)
% 1.26/1.19 % (14547)First to succeed.
% 1.38/1.20 % (14547)Refutation found. Thanks to Tanya!
% 1.38/1.20 % SZS status Theorem for DTF2THF_14445
% 1.38/1.20 % SZS output start Proof for DTF2THF_14445
% 1.38/1.20 thf(func_def_0, type, cP: $i > $i > $o).
% 1.38/1.20 thf(func_def_1, type, cE: ($i > $o) > $i).
% 1.38/1.20 thf(func_def_9, type, ph1: !>[X0: $tType]:(X0)).
% 1.38/1.20 thf(f12,plain,(
% 1.38/1.20 $false),
% 1.38/1.20 inference(trivial_inequality_removal,[status(thm)],[f11])).
% 1.38/1.20 thf(f11,plain,(
% 1.38/1.20 ($true != $true)),
% 1.38/1.20 inference(superposition,[status(thm)],[f8,f10])).
% 1.38/1.20 thf(f10,plain,(
% 1.38/1.20 ( ! [X0 : $i] : (($true = (cP @ X0 @ (cE @ (cP @ X0))))) )),
% 1.38/1.20 inference(beta_eta_normalization,[status(thm)],[f9])).
% 1.38/1.20 thf(f9,plain,(
% 1.38/1.20 ( ! [X0 : $i] : (((cP @ X0 @ (cE @ (^[Y0 : $i]: (cP @ X0 @ Y0)))) = $true)) )),
% 1.38/1.20 inference(cnf_transformation,[status(thm)],[f7])).
% 1.38/1.20 thf(f7,plain,(
% 1.38/1.20 ! [X0 : $i] : ((cP @ X0 @ (cE @ (^[Y0 : $i]: (cP @ X0 @ Y0)))) = $true) & ! [X1 : $i > $i] : ($true != (cP @ (cE @ (^[Y0 : $i]: (~ (cP @ Y0 @ (X1 @ Y0))))) @ (X1 @ (cE @ (^[Y0 : $i]: (~ (cP @ Y0 @ (X1 @ Y0))))))))),
% 1.38/1.20 inference(flattening,[status(thm)],[f6])).
% 1.38/1.20 thf(f6,plain,(
% 1.38/1.20 ~~(! [X0 : $i] : ((cP @ X0 @ (cE @ (^[Y0 : $i]: (cP @ X0 @ Y0)))) = $true) & ! [X1 : $i > $i] : ~($true = (cP @ (cE @ (^[Y0 : $i]: (~ (cP @ Y0 @ (X1 @ Y0))))) @ (X1 @ (cE @ (^[Y0 : $i]: (~ (cP @ Y0 @ (X1 @ Y0)))))))))),
% 1.38/1.20 inference(rectify,[status(thm)],[f5])).
% 1.38/1.20 thf(f5,plain,(
% 1.38/1.20 ~~(! [X0 : $i] : ((cP @ X0 @ (cE @ (^[Y0 : $i]: (cP @ X0 @ Y0)))) = $true) & ! [X2 : $i > $i] : ~($true = (cP @ (cE @ (^[Y0 : $i]: (~ (cP @ Y0 @ (X2 @ Y0))))) @ (X2 @ (cE @ (^[Y0 : $i]: (~ (cP @ Y0 @ (X2 @ Y0)))))))))),
% 1.38/1.20 inference(fool_elimination,[status(thm)],[f4])).
% 1.38/1.20 thf(f4,plain,(
% 1.38/1.20 ~~(! [X0 : $i] : (cP @ X0 @ (cE @ (^[X1 : $i] : (cP @ X0 @ X1)))) & ! [X2 : $i > $i] : ~(cP @ (cE @ (^[X3 : $i] : (~(cP @ X3 @ (X2 @ X3))))) @ (X2 @ (cE @ (^[X4 : $i] : (~(cP @ X4 @ (X2 @ X4))))))))),
% 1.38/1.20 inference(rectify,[status(thm)],[f2])).
% 1.38/1.20 thf(f2,negated_conjecture,(
% 1.38/1.20 ~~(! [X0 : $i] : (cP @ X0 @ (cE @ (^[X1 : $i] : (cP @ X0 @ X1)))) & ! [X2 : $i > $i] : ~(cP @ (cE @ (^[X0 : $i] : (~(cP @ X0 @ (X2 @ X0))))) @ (X2 @ (cE @ (^[X0 : $i] : (~(cP @ X0 @ (X2 @ X0))))))))),
% 1.38/1.20 inference(negated_conjecture,[status(cth)],[f1])).
% 1.38/1.20 thf(f1,conjecture,(
% 1.38/1.20 ~(! [X0 : $i] : (cP @ X0 @ (cE @ (^[X1 : $i] : (cP @ X0 @ X1)))) & ! [X2 : $i > $i] : ~(cP @ (cE @ (^[X0 : $i] : (~(cP @ X0 @ (X2 @ X0))))) @ (X2 @ (cE @ (^[X0 : $i] : (~(cP @ X0 @ (X2 @ X0))))))))),
% 1.38/1.20 file('/export/starexec/sandbox2/tmp/tmp.afu61bwxoH/DTF2THF_14445.p',cTHM19SK1)).
% 1.38/1.20 thf(f8,plain,(
% 1.38/1.20 ( ! [X1 : $i > $i] : (($true != (cP @ (cE @ (^[Y0 : $i]: (~ (cP @ Y0 @ (X1 @ Y0))))) @ (X1 @ (cE @ (^[Y0 : $i]: (~ (cP @ Y0 @ (X1 @ Y0))))))))) )),
% 1.38/1.20 inference(cnf_transformation,[status(thm)],[f7])).
% 1.38/1.20 % SZS output end Proof for DTF2THF_14445
% 1.38/1.20 % (14547)------------------------------
% 1.38/1.20 % (14547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.38/1.20 % (14547)Termination reason: Refutation
% 1.38/1.20
% 1.38/1.20 % (14547)Memory used [KB]: 5500
% 1.38/1.20 % (14547)Time elapsed: 0.003 s
% 1.38/1.20 % (14547)Instructions burned: 2 (million)
% 1.38/1.20 % (14547)------------------------------
% 1.38/1.20 % (14547)------------------------------
% 1.38/1.20 % (14546)Success in time 0.012 s
%------------------------------------------------------------------------------