%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO553^1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.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 09:54:32 AM UTC 2026
% Result : Theorem 1.47s 1.27s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 8 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 9 ( 8 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 33 ( 7 ~; 0 |; 0 &; 25 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 17 ( 0 ^; 10 !; 7 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_3,type,
sK0: ( $i > $i > $i ) > $i ).
thf(func_def_4,type,
sK1: ( $i > $i > $i ) > $i ).
thf(func_def_6,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f9,plain,
$false,
inference(equality_resolution,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $i > $i > $i] :
( ( sK0 @ X0 )
!= ( X0 @ ( sK1 @ X0 ) @ ( sK0 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $i > $i > $i] :
( ( sK0 @ X0 )
!= ( X0 @ ( sK1 @ X0 ) @ ( sK0 @ X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f5,f6]) ).
thf(f6,plain,
! [X0: $i > $i > $i] :
( ? [X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
!= X1 )
=> ( ( sK0 @ X0 )
!= ( X0 @ ( sK1 @ X0 ) @ ( sK0 @ X0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f5,plain,
! [X0: $i > $i > $i] :
? [X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
!= X1 ),
inference(ennf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
~ ? [X0: $i > $i > $i] :
! [X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
= X1 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ? [X0: $i > $i > $i] :
! [X2: $i,X1: $i] :
( ( X0 @ X1 @ X2 )
= X2 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
? [X0: $i > $i > $i] :
! [X2: $i,X1: $i] :
( ( X0 @ X1 @ X2 )
= X2 ),
file('/export/starexec/sandbox2/tmp/tmp.teEr5MPw2F/DTF2THF_28026.p',claim) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO553^1 : TPTP v9.2.1. Released v5.2.0.
% 0.11/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n014.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 14:33:42 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.45 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SYO553^1 : TPTP v9.2.1. Released v5.2.0.
% 0.28/0.46 % Domain : Syntactic
% 0.28/0.46 % Problem : The second projection exists.
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English : There is a binary function that returns its second argument.
% 0.28/0.46
% 0.28/0.46 % Refs : [Bro11] Brown E. (2011), Email to Geoff Sutcliffe
% 0.28/0.46 % Source : [Bro11]
% 0.28/0.46 % Names : PROJ2 [Bro11]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.46 v8.1.0, 0.45 v7.5.0, 0.14 v7.4.0, 0.00 v6.2.0, 0.29 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.2.0
% 0.28/0.46 % Syntax : Number of formulae : 1 ( 1 unt; 0 typ; 0 def)
% 0.28/0.46 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.28/0.46 % Number of connectives : 2 ( 0 ~; 0 |; 0 &; 2 @)
% 0.28/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 4 ( 4 avg)
% 0.28/0.46 % Number of types : 1 ( 0 usr)
% 0.28/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.28/0.46 % Number of variables : 3 ( 0 ^; 2 !; 1 ?; 3 :)
% 0.28/0.46 % SPC : TH0_THM_EQU_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : This simple problem tests higher-order instantiations.
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(claim,conjecture,
% 0.28/0.46 ? [F: $i > $i > $i] :
% 0.28/0.46 ! [X: $i,Y: $i] :
% 0.28/0.46 ( ( F @ X @ Y )
% 0.28/0.46 = Y ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 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 14:33:43 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.teEr5MPw2F/DTF2DTF28026.p
% See solution above
% 1.47/1.25 ------------------------
% 1.47/1.25 ---- Cleaned THF ---
% 1.47/1.26 thf(claim,conjecture,
% 1.47/1.26 ? [F: $i > $i > $i] :
% 1.47/1.26 ! [X: $i,Y: $i] :
% 1.47/1.26 ( ( F @ X @ Y )
% 1.47/1.26 = Y ) ).
% 1.47/1.26 ------------------------
% 1.47/1.27 % (28229)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_28026 for (2999ds/4Mi)
% 1.47/1.27 % (28228)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28026 for (2999ds/183Mi)
% 1.47/1.27 % (28229)First to succeed.
% 1.47/1.27 % (28228)Also succeeded, but the first one will report.
% 1.47/1.27 % (28229)Refutation found. Thanks to Tanya!
% 1.47/1.27 % SZS status Theorem for DTF2THF_28026
% 1.47/1.27 % SZS output start Proof for DTF2THF_28026
% 1.47/1.27 thf(func_def_3, type, sK0: ($i > $i > $i) > $i).
% 1.47/1.27 thf(func_def_4, type, sK1: ($i > $i > $i) > $i).
% 1.47/1.27 thf(func_def_6, type, ph3: !>[X0: $tType]:(X0)).
% 1.47/1.27 thf(f9,plain,(
% 1.47/1.27 $false),
% 1.47/1.27 inference(equality_resolution,[status(thm)],[f8])).
% 1.47/1.27 thf(f8,plain,(
% 1.47/1.27 ( ! [X0 : $i > $i > $i] : (((sK0 @ X0) != (X0 @ (sK1 @ X0) @ (sK0 @ X0)))) )),
% 1.47/1.27 inference(cnf_transformation,[status(thm)],[f7])).
% 1.47/1.27 thf(f7,plain,(
% 1.47/1.27 ! [X0 : $i > $i > $i] : ((sK0 @ X0) != (X0 @ (sK1 @ X0) @ (sK0 @ X0)))),
% 1.47/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f5,f6])).
% 1.47/1.27 thf(f6,plain,(
% 1.47/1.27 ! [X0 : $i > $i > $i] : (? [X1 : $i,X2 : $i] : ((X0 @ X2 @ X1) != X1) => ((sK0 @ X0) != (X0 @ (sK1 @ X0) @ (sK0 @ X0))))),
% 1.47/1.27 introduced(definition,[],[choice_axiom])).
% 1.47/1.27 thf(f5,plain,(
% 1.47/1.27 ! [X0 : $i > $i > $i] : ? [X1 : $i,X2 : $i] : ((X0 @ X2 @ X1) != X1)),
% 1.47/1.27 inference(ennf_transformation,[status(thm)],[f4])).
% 1.47/1.27 thf(f4,plain,(
% 1.47/1.27 ~? [X0 : $i > $i > $i] : ! [X1 : $i,X2 : $i] : ((X0 @ X2 @ X1) = X1)),
% 1.47/1.27 inference(rectify,[status(thm)],[f2])).
% 1.47/1.27 thf(f2,negated_conjecture,(
% 1.47/1.27 ~? [X0 : $i > $i > $i] : ! [X2 : $i,X1 : $i] : ((X0 @ X1 @ X2) = X2)),
% 1.47/1.27 inference(negated_conjecture,[status(cth)],[f1])).
% 1.47/1.27 thf(f1,conjecture,(
% 1.47/1.27 ? [X0 : $i > $i > $i] : ! [X2 : $i,X1 : $i] : ((X0 @ X1 @ X2) = X2)),
% 1.47/1.27 file('/export/starexec/sandbox2/tmp/tmp.teEr5MPw2F/DTF2THF_28026.p',claim)).
% 1.47/1.27 % SZS output end Proof for DTF2THF_28026
% 1.47/1.27 % (28229)------------------------------
% 1.47/1.27 % (28229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.27 % (28229)Termination reason: Refutation
% 1.47/1.27
% 1.47/1.27 % (28229)Memory used [KB]: 5500
% 1.47/1.27 % (28229)Time elapsed: 0.002 s
% 1.47/1.27 % (28229)Instructions burned: 1 (million)
% 1.47/1.27 % (28229)------------------------------
% 1.47/1.27 % (28229)------------------------------
% 1.47/1.27 % (28227)Success in time 0.012 s
%------------------------------------------------------------------------------