%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO355^5 : 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 : n031.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 09:54:01 AM UTC 2026
% Result : Theorem 1.49s 1.29s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 11 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 20 ( 17 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 9 ~; 0 |; 3 &; 2 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 0 ^; 20 !; 6 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_2,type,
sK0: $i > $i ).
thf(func_def_3,type,
sK1: $i > $i ).
thf(func_def_5,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f12,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f11,f10]) ).
thf(f10,plain,
! [X0: $i,X1: $i] : ( X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X0: $i,X1: $i] : ( X0 = X1 )
& ( sK0 != sK1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7]) ).
thf(f7,plain,
( ? [X2: $i > $i,X3: $i > $i] : ( X2 != X3 )
=> ( sK0 != sK1 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
( ! [X0: $i,X1: $i] : ( X0 = X1 )
& ? [X2: $i > $i,X3: $i > $i] : ( X2 != X3 ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
( ! [X1: $i,X0: $i] : ( X0 = X1 )
& ? [X3: $i > $i,X2: $i > $i] : ( X2 != X3 ) ),
inference(ennf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X1: $i,X0: $i] : ( X0 = X1 )
=> ! [X2: $i > $i,X3: $i > $i] : ( X2 = X3 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X1: $i,X0: $i] : ( X0 = X1 )
=> ! [X3: $i > $i,X2: $i > $i] : ( X2 = X3 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X1: $i,X0: $i] : ( X0 = X1 )
=> ! [X3: $i > $i,X2: $i > $i] : ( X2 = X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.nixWrXfAQI/DTF2THF_27096.p',cTHM613) ).
thf(f11,plain,
( ( sK0 @ sK4 )
!= ( sK1 @ sK4 ) ),
inference(negative_extensionality,[status(thm)],[f9]) ).
thf(f9,plain,
sK0 != sK1,
inference(cnf_transformation,[status(thm)],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO355^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n031.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 14:29:33 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.47 ---- Original DTF file ---
% 0.20/0.47 thf(spec,logic,$$dhol).
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 % File : SYO355^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.47 % Domain : Syntactic
% 0.20/0.47 % Problem : TPS problem THM613
% 0.20/0.47 % Version : Especial.
% 0.20/0.47 % English : If there's one individual, then there's only one function.
% 0.20/0.47
% 0.20/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.47 % Source : [Bro09]
% 0.20/0.47 % Names : tps_0180 [Bro09]
% 0.20/0.47 % : THM613 [TPS]
% 0.20/0.47
% 0.20/0.47 % Status : Theorem
% 0.20/0.47 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 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, 0.40 v4.1.0, 0.33 v4.0.0
% 0.20/0.47 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.20/0.47 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.20/0.47 % Maximal formula atoms : 2 ( 2 avg)
% 0.20/0.47 % Number of connectives : 1 ( 0 ~; 0 |; 0 &; 0 @)
% 0.20/0.47 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.20/0.47 % Maximal formula depth : 4 ( 4 avg)
% 0.20/0.47 % Number of types : 1 ( 0 usr)
% 0.20/0.47 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.20/0.47 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.20/0.47 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.20/0.47 % SPC : TH0_THM_EQU_NAR
% 0.20/0.47
% 0.20/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 thf(cTHM613,conjecture,
% 0.20/0.47 ( ! [Xa: $i,Xb: $i] : ( Xa = Xb )
% 0.20/0.47 => ! [Xf: $i > $i,Xg: $i > $i] : ( Xf = Xg ) ) ).
% 0.20/0.47
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 ------------------------
% 1.49/1.27 ---- Embedded in THF ---
% 1.49/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.27 %%% Generated on Tue Feb 24 14:29:34 EST 2026
% 1.49/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.27 %%% Logic specification used:
% 1.49/1.27 %%% thf(spec, logic, $$dhol).
% 1.49/1.27
% 1.49/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.nixWrXfAQI/DTF2DTF27096.p
% See solution above
% 1.49/1.27 ------------------------
% 1.49/1.28 ---- Cleaned THF ---
% 1.49/1.28 thf(cTHM613,conjecture,
% 1.49/1.28 ( ! [Xa: $i,Xb: $i] : ( Xa = Xb )
% 1.49/1.28 => ! [Xf: $i > $i,Xg: $i > $i] : ( Xf = Xg ) ) ).
% 1.49/1.28 ------------------------
% 1.49/1.29 % (27290)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_27096 for (3000ds/275Mi)
% 1.49/1.29 % (27288)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27096 for (3000ds/2Mi)
% 1.49/1.29 % (27285)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27096 for (3000ds/183Mi)
% 1.49/1.29 % (27290)First to succeed.
% 1.49/1.29 % (27285)Also succeeded, but the first one will report.
% 1.49/1.29 % (27290)Refutation found. Thanks to Tanya!
% 1.49/1.29 % SZS status Theorem for DTF2THF_27096
% 1.49/1.29 % SZS output start Proof for DTF2THF_27096
% 1.49/1.29 thf(func_def_2, type, sK0: $i > $i).
% 1.49/1.29 thf(func_def_3, type, sK1: $i > $i).
% 1.49/1.29 thf(func_def_5, type, ph3: !>[X0: $tType]:(X0)).
% 1.49/1.29 thf(f12,plain,(
% 1.49/1.29 $false),
% 1.49/1.29 inference(subsumption_resolution,[status(thm)],[f11,f10])).
% 1.49/1.29 thf(f10,plain,(
% 1.49/1.29 ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) )),
% 1.49/1.29 inference(cnf_transformation,[status(thm)],[f8])).
% 1.49/1.29 thf(f8,plain,(
% 1.49/1.29 ! [X0 : $i,X1 : $i] : (X0 = X1) & (sK0 != sK1)),
% 1.49/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f7])).
% 1.49/1.29 thf(f7,plain,(
% 1.49/1.29 ? [X2 : $i > $i,X3 : $i > $i] : (X2 != X3) => (sK0 != sK1)),
% 1.49/1.29 introduced(definition,[],[choice_axiom])).
% 1.49/1.29 thf(f6,plain,(
% 1.49/1.29 ! [X0 : $i,X1 : $i] : (X0 = X1) & ? [X2 : $i > $i,X3 : $i > $i] : (X2 != X3)),
% 1.49/1.29 inference(rectify,[status(thm)],[f5])).
% 1.49/1.29 thf(f5,plain,(
% 1.49/1.29 ! [X1 : $i,X0 : $i] : (X0 = X1) & ? [X3 : $i > $i,X2 : $i > $i] : (X2 != X3)),
% 1.49/1.29 inference(ennf_transformation,[status(thm)],[f4])).
% 1.49/1.29 thf(f4,plain,(
% 1.49/1.29 ~(! [X1 : $i,X0 : $i] : (X0 = X1) => ! [X2 : $i > $i,X3 : $i > $i] : (X2 = X3))),
% 1.49/1.29 inference(rectify,[status(thm)],[f2])).
% 1.49/1.29 thf(f2,negated_conjecture,(
% 1.49/1.29 ~(! [X1 : $i,X0 : $i] : (X0 = X1) => ! [X3 : $i > $i,X2 : $i > $i] : (X2 = X3))),
% 1.49/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.49/1.29 thf(f1,conjecture,(
% 1.49/1.29 ! [X1 : $i,X0 : $i] : (X0 = X1) => ! [X3 : $i > $i,X2 : $i > $i] : (X2 = X3)),
% 1.49/1.29 file('/export/starexec/sandbox/tmp/tmp.nixWrXfAQI/DTF2THF_27096.p',cTHM613)).
% 1.49/1.29 thf(f11,plain,(
% 1.49/1.29 ((sK0 @ sK4) != (sK1 @ sK4))),
% 1.49/1.29 inference(negative_extensionality,[status(thm)],[f9])).
% 1.49/1.29 thf(f9,plain,(
% 1.49/1.29 (sK0 != sK1)),
% 1.49/1.29 inference(cnf_transformation,[status(thm)],[f8])).
% 1.49/1.29 % SZS output end Proof for DTF2THF_27096
% 1.49/1.29 % (27290)------------------------------
% 1.49/1.29 % (27290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.29 % (27290)Termination reason: Refutation
% 1.49/1.29
% 1.49/1.29 % (27290)Memory used [KB]: 5373
% 1.49/1.29 % (27290)Time elapsed: 0.002 s
% 1.49/1.29 % (27290)------------------------------
% 1.49/1.29 % (27290)------------------------------
% 1.49/1.29 % (27284)Success in time 0.002 s
%------------------------------------------------------------------------------