%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYN731^5 : 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 : n010.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 09:51:23 AM UTC 2026
% Result : Theorem 1.48s 1.28s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 16 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 83 ( 8 ~; 1 |; 3 &; 66 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 2 con; 0-3 aty)
% Number of variables : 38 ( 0 ^; 23 !; 15 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cP: $i > $i > $i > $o ).
thf(func_def_4,type,
sK0: $i > $i > $i ).
thf(f20,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f19]) ).
thf(f19,plain,
$true = $false,
inference(superposition,[status(thm)],[f13,f10]) ).
thf(f10,plain,
! [X2: $i,X0: $i] :
( $true
= ( cP @ X0 @ X2 @ ( sK0 @ X2 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $i] :
( ! [X1: $i] :
( $true
!= ( cP @ X1 @ X1 @ X0 ) )
& ! [X2: $i] :
( $true
= ( cP @ X0 @ X2 @ ( sK0 @ X2 @ X0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8]) ).
thf(f8,plain,
! [X0: $i,X2: $i] :
( ? [X3: $i] :
( $true
= ( cP @ X0 @ X2 @ X3 ) )
=> ( $true
= ( cP @ X0 @ X2 @ ( sK0 @ X2 @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
! [X0: $i] :
( ! [X1: $i] :
( $true
!= ( cP @ X1 @ X1 @ X0 ) )
& ! [X2: $i] :
? [X3: $i] :
( $true
= ( cP @ X0 @ X2 @ X3 ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $i] :
( ! [X3: $i] :
( ( cP @ X3 @ X3 @ X0 )
!= $true )
& ! [X1: $i] :
? [X2: $i] :
( ( cP @ X0 @ X1 @ X2 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ? [X0: $i] :
( ! [X1: $i] :
? [X2: $i] :
( ( cP @ X0 @ X1 @ X2 )
= $true )
=> ? [X3: $i] :
( ( cP @ X3 @ X3 @ X0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: $i] :
( ! [X1: $i] :
? [X2: $i] : ( cP @ X0 @ X1 @ X2 )
=> ? [X3: $i] : ( cP @ X3 @ X3 @ X0 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: $i] :
( ! [X1: $i] :
? [X2: $i] : ( cP @ X0 @ X1 @ X2 )
=> ? [X3: $i] : ( cP @ X3 @ X3 @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: $i] :
( ! [X1: $i] :
? [X2: $i] : ( cP @ X0 @ X1 @ X2 )
=> ? [X3: $i] : ( cP @ X3 @ X3 @ X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.BtEqZPauKh/DTF2THF_15250.p',cX2150) ).
thf(f13,plain,
! [X0: $i,X1: $i] :
( $false
= ( cP @ X1 @ X1 @ X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( $false
= ( cP @ X1 @ X1 @ X0 ) ) ),
inference(fool_paramodulation,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i,X1: $i] :
( $true
!= ( cP @ X1 @ X1 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN731^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n010.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 14:15:18 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.26/0.46 ---- Original DTF file ---
% 0.26/0.46 thf(spec,logic,$$dhol).
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 % File : SYN731^5 : TPTP v9.2.1. Released v4.0.0.
% 0.26/0.46 % Domain : Syntactic
% 0.26/0.46 % Problem : TPS problem X2150
% 0.26/0.46 % Version : Especial.
% 0.26/0.46 % English :
% 0.26/0.46
% 0.26/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.26/0.46 % Source : [Bro09]
% 0.26/0.46 % Names : tps_0095 [Bro09]
% 0.26/0.46 % : X2150 [TPS]
% 0.26/0.46
% 0.26/0.46 % Status : Theorem
% 0.26/0.46 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 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 v6.0.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.26/0.46 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.26/0.46 % Number of atoms : 2 ( 0 equ; 0 cnn)
% 0.26/0.46 % Maximal formula atoms : 2 ( 2 avg)
% 0.26/0.46 % Number of connectives : 7 ( 0 ~; 0 |; 0 &; 6 @)
% 0.26/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.26/0.46 % Maximal formula depth : 8 ( 8 avg)
% 0.26/0.46 % Number of types : 2 ( 0 usr)
% 0.26/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.26/0.46 % Number of symbols : 1 ( 1 usr; 0 con; 3-3 aty)
% 0.26/0.46 % Number of variables : 4 ( 0 ^; 1 !; 3 ?; 4 :)
% 0.26/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.26/0.46
% 0.26/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.26/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.26/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.26/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.26/0.46 % :
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 thf(cP,type,
% 0.26/0.46 cP: $i > $i > $i > $o ).
% 0.26/0.46
% 0.26/0.46 thf(cX2150,conjecture,
% 0.26/0.46 ? [W: $i] :
% 0.26/0.46 ( ! [X: $i] :
% 0.26/0.46 ? [Y: $i] : ( cP @ W @ X @ Y )
% 0.26/0.46 => ? [Z: $i] : ( cP @ Z @ Z @ W ) ) ).
% 0.26/0.46
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 ------------------------
% 1.48/1.26 ---- Embedded in THF ---
% 1.48/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.26 %%% Generated on Tue Feb 24 14:15:19 EST 2026
% 1.48/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.26 %%% Logic specification used:
% 1.48/1.26 %%% thf(spec, logic, $$dhol).
% 1.48/1.26
% 1.48/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.BtEqZPauKh/DTF2DTF15250.p
% See solution above
% 1.48/1.26 ------------------------
% 1.48/1.27 ---- Cleaned THF ---
% 1.48/1.27 thf(cP,type,
% 1.48/1.27 cP: $i > $i > $i > $o ).
% 1.48/1.27
% 1.48/1.27 thf(cX2150,conjecture,
% 1.48/1.27 ? [W: $i] :
% 1.48/1.27 ( ! [X: $i] :
% 1.48/1.27 ? [Y: $i] : ( cP @ W @ X @ Y )
% 1.48/1.27 => ? [Z: $i] : ( cP @ Z @ Z @ W ) ) ).
% 1.48/1.27 ------------------------
% 1.48/1.28 % (15469)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_15250 for (2999ds/4Mi)
% 1.48/1.28 % (15469)First to succeed.
% 1.48/1.28 % (15469)Refutation found. Thanks to Tanya!
% 1.48/1.28 % SZS status Theorem for DTF2THF_15250
% 1.48/1.28 % SZS output start Proof for DTF2THF_15250
% 1.48/1.28 thf(func_def_0, type, cP: $i > $i > $i > $o).
% 1.48/1.28 thf(func_def_4, type, sK0: $i > $i > $i).
% 1.48/1.28 thf(f20,plain,(
% 1.48/1.28 $false),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f19])).
% 1.48/1.28 thf(f19,plain,(
% 1.48/1.28 ($true = $false)),
% 1.48/1.28 inference(superposition,[status(thm)],[f13,f10])).
% 1.48/1.28 thf(f10,plain,(
% 1.48/1.28 ( ! [X2 : $i,X0 : $i] : (($true = (cP @ X0 @ X2 @ (sK0 @ X2 @ X0)))) )),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f9])).
% 1.48/1.28 thf(f9,plain,(
% 1.48/1.28 ! [X0 : $i] : (! [X1 : $i] : ($true != (cP @ X1 @ X1 @ X0)) & ! [X2 : $i] : ($true = (cP @ X0 @ X2 @ (sK0 @ X2 @ X0))))),
% 1.48/1.28 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8])).
% 1.48/1.28 thf(f8,plain,(
% 1.48/1.28 ! [X0 : $i,X2 : $i] : (? [X3 : $i] : ($true = (cP @ X0 @ X2 @ X3)) => ($true = (cP @ X0 @ X2 @ (sK0 @ X2 @ X0))))),
% 1.48/1.28 introduced(definition,[],[choice_axiom])).
% 1.48/1.28 thf(f7,plain,(
% 1.48/1.28 ! [X0 : $i] : (! [X1 : $i] : ($true != (cP @ X1 @ X1 @ X0)) & ! [X2 : $i] : ? [X3 : $i] : ($true = (cP @ X0 @ X2 @ X3)))),
% 1.48/1.28 inference(rectify,[status(thm)],[f6])).
% 1.48/1.28 thf(f6,plain,(
% 1.48/1.28 ! [X0 : $i] : (! [X3 : $i] : ((cP @ X3 @ X3 @ X0) != $true) & ! [X1 : $i] : ? [X2 : $i] : ((cP @ X0 @ X1 @ X2) = $true))),
% 1.48/1.28 inference(ennf_transformation,[status(thm)],[f5])).
% 1.48/1.28 thf(f5,plain,(
% 1.48/1.28 ~? [X0 : $i] : (! [X1 : $i] : ? [X2 : $i] : ((cP @ X0 @ X1 @ X2) = $true) => ? [X3 : $i] : ((cP @ X3 @ X3 @ X0) = $true))),
% 1.48/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.48/1.28 thf(f4,plain,(
% 1.48/1.28 ~? [X0 : $i] : (! [X1 : $i] : ? [X2 : $i] : (cP @ X0 @ X1 @ X2) => ? [X3 : $i] : (cP @ X3 @ X3 @ X0))),
% 1.48/1.28 inference(rectify,[status(thm)],[f2])).
% 1.48/1.28 thf(f2,negated_conjecture,(
% 1.48/1.28 ~? [X0 : $i] : (! [X1 : $i] : ? [X2 : $i] : (cP @ X0 @ X1 @ X2) => ? [X3 : $i] : (cP @ X3 @ X3 @ X0))),
% 1.48/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.48/1.28 thf(f1,conjecture,(
% 1.48/1.28 ? [X0 : $i] : (! [X1 : $i] : ? [X2 : $i] : (cP @ X0 @ X1 @ X2) => ? [X3 : $i] : (cP @ X3 @ X3 @ X0))),
% 1.48/1.28 file('/export/starexec/sandbox2/tmp/tmp.BtEqZPauKh/DTF2THF_15250.p',cX2150)).
% 1.48/1.28 thf(f13,plain,(
% 1.48/1.28 ( ! [X0 : $i,X1 : $i] : (($false = (cP @ X1 @ X1 @ X0))) )),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f12])).
% 1.48/1.28 thf(f12,plain,(
% 1.48/1.28 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ($false = (cP @ X1 @ X1 @ X0))) )),
% 1.48/1.28 inference(fool_paramodulation,[status(thm)],[f11])).
% 1.48/1.28 thf(f11,plain,(
% 1.48/1.28 ( ! [X0 : $i,X1 : $i] : (($true != (cP @ X1 @ X1 @ X0))) )),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f9])).
% 1.48/1.28 % SZS output end Proof for DTF2THF_15250
% 1.48/1.28 % (15469)------------------------------
% 1.48/1.28 % (15469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (15469)Termination reason: Refutation
% 1.48/1.28
% 1.48/1.28 % (15469)Memory used [KB]: 5500
% 1.48/1.28 % (15469)Time elapsed: 0.003 s
% 1.48/1.28 % (15469)Instructions burned: 1 (million)
% 1.48/1.28 % (15469)------------------------------
% 1.48/1.28 % (15469)------------------------------
% 1.48/1.28 % (15467)Success in time 0.012 s
%------------------------------------------------------------------------------