%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU882^5 : 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 : n025.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 09:37:39 AM UTC 2026
% Result : Theorem 1.61s 1.30s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 9 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 13 ( 9 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 8 ~; 0 |; 0 &; 9 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 2 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 0 ^; 15 !; 9 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_5,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f10,plain,
$false,
inference(equality_resolution,[status(thm)],[f9]) ).
thf(f9,plain,
! [X2: $i,X1: $i > $i] :
( ( X1 @ X2 )
!= sK0 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X1: $i > $i,X2: $i] :
( ( X1 @ X2 )
!= sK0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: $i] :
! [X1: $i > $i,X2: $i] :
( ( X1 @ X2 )
!= X0 )
=> ! [X2: $i,X1: $i > $i] :
( ( X1 @ X2 )
!= sK0 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: $i] :
! [X1: $i > $i,X2: $i] :
( ( X1 @ X2 )
!= X0 ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
? [X0: $i] :
! [X2: $i > $i,X1: $i] :
( ( X2 @ X1 )
!= X0 ),
inference(ennf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i] :
? [X2: $i > $i,X1: $i] :
( ( X2 @ X1 )
= X0 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: $i] :
? [X2: $i,X1: $i > $i] :
( ( X1 @ X2 )
= X0 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: $i] :
? [X2: $i,X1: $i > $i] :
( ( X1 @ X2 )
= X0 ),
file('/export/starexec/sandbox/tmp/tmp.SjG4dn3XhK/DTF2THF_10544.p',cTHM139_pme) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU882^5 : 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
% 0.18/0.34 % Computer : n025.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 12:36:12 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SEU882^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.46 % Domain : Set Theory
% 0.28/0.46 % Problem : TPS problem THM139
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English : Every object is in the range of some function.
% 0.28/0.46
% 0.28/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.46 % Source : [Bro09]
% 0.28/0.46 % Names : tps_0037 [Bro09]
% 0.28/0.46 % : THM139 [TPS]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.0
% 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 : 1 ( 0 ~; 0 |; 0 &; 1 @)
% 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 : 1 ( 1 >; 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 ^; 1 !; 2 ?; 3 :)
% 0.28/0.46 % SPC : TH0_THM_EQU_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.28/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.28/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.28/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.28/0.46 % : Polymorphic definitions expanded.
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(cTHM139_pme,conjecture,
% 0.28/0.46 ! [Xy: $i] :
% 0.28/0.46 ? [Xf: $i > $i,Xx: $i] :
% 0.28/0.46 ( ( Xf @ Xx )
% 0.28/0.46 = Xy ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 1.47/1.26 ---- Embedded in THF ---
% 1.47/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.26 %%% Generated on Tue Feb 24 12:36:13 EST 2026
% 1.47/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.26 %%% Logic specification used:
% 1.47/1.26 %%% thf(spec, logic, $$dhol).
% 1.47/1.26
% 1.47/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.SjG4dn3XhK/DTF2DTF10544.p
% See solution above
% 1.47/1.26 ------------------------
% 1.47/1.27 ---- Cleaned THF ---
% 1.47/1.27 thf(cTHM139_pme,conjecture,
% 1.47/1.27 ! [Xy: $i] :
% 1.47/1.27 ? [Xf: $i > $i,Xx: $i] :
% 1.47/1.27 ( ( Xf @ Xx )
% 1.47/1.27 = Xy ) ).
% 1.47/1.27 ------------------------
% 1.47/1.29 % (10826)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10544 for (2999ds/2Mi)
% 1.47/1.29 % (10826)Refutation not found, incomplete strategy
% 1.47/1.29 % (10826)------------------------------
% 1.47/1.29 % (10826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.29 % (10826)Termination reason: Refutation not found, incomplete strategy
% 1.47/1.29
% 1.47/1.29
% 1.47/1.29 % (10826)Memory used [KB]: 5373
% 1.47/1.29 % (10826)Time elapsed: 0.002 s
% 1.47/1.29 % (10826)Instructions burned: 1 (million)
% 1.47/1.29 % (10826)------------------------------
% 1.47/1.29 % (10826)------------------------------
% 1.47/1.29 % (10823)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10544 for (2999ds/183Mi)
% 1.47/1.29 % (10824)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_10544 for (2999ds/4Mi)
% 1.47/1.29 % (10825)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_10544 for (2999ds/27Mi)
% 1.47/1.29 % (10827)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_10544 for (2999ds/2Mi)
% 1.47/1.30 % (10828)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_10544 for (2999ds/275Mi)
% 1.47/1.30 % (10829)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10544 for (2999ds/18Mi)
% 1.47/1.30 % (10823)First to succeed.
% 1.47/1.30 % (10825)Refutation not found, incomplete strategy
% 1.47/1.30 % (10825)------------------------------
% 1.47/1.30 % (10825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.30 % (10825)Termination reason: Refutation not found, incomplete strategy
% 1.47/1.30
% 1.47/1.30
% 1.47/1.30 % (10825)Memory used [KB]: 5373
% 1.47/1.30 % (10825)Time elapsed: 0.003 s
% 1.47/1.30 % (10825)Instructions burned: 1 (million)
% 1.47/1.30 % (10825)------------------------------
% 1.47/1.30 % (10825)------------------------------
% 1.47/1.30 % (10828)Refutation not found, incomplete strategy
% 1.47/1.30 % (10828)------------------------------
% 1.47/1.30 % (10828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.30 % (10828)Termination reason: Refutation not found, incomplete strategy
% 1.47/1.30
% 1.47/1.30
% 1.47/1.30 % (10828)Memory used [KB]: 5373
% 1.47/1.30 % (10828)Time elapsed: 0.003 s
% 1.47/1.30 % (10828)Instructions burned: 1 (million)
% 1.47/1.30 % (10828)------------------------------
% 1.47/1.30 % (10828)------------------------------
% 1.47/1.30 % (10824)Also succeeded, but the first one will report.
% 1.61/1.30 % (10827)Refutation not found, incomplete strategy
% 1.61/1.30 % (10827)------------------------------
% 1.61/1.30 % (10827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (10827)Termination reason: Refutation not found, incomplete strategy
% 1.61/1.30
% 1.61/1.30
% 1.61/1.30 % (10827)Memory used [KB]: 5500
% 1.61/1.30 % (10827)Time elapsed: 0.003 s
% 1.61/1.30 % (10827)Instructions burned: 1 (million)
% 1.61/1.30 % (10827)------------------------------
% 1.61/1.30 % (10827)------------------------------
% 1.61/1.30 % (10829)Also succeeded, but the first one will report.
% 1.61/1.30 % (10823)Refutation found. Thanks to Tanya!
% 1.61/1.30 % SZS status Theorem for DTF2THF_10544
% 1.61/1.30 % SZS output start Proof for DTF2THF_10544
% 1.61/1.30 thf(func_def_5, type, ph2: !>[X0: $tType]:(X0)).
% 1.61/1.30 thf(f10,plain,(
% 1.61/1.30 $false),
% 1.61/1.30 inference(equality_resolution,[status(thm)],[f9])).
% 1.61/1.30 thf(f9,plain,(
% 1.61/1.30 ( ! [X2 : $i,X1 : $i > $i] : (((X1 @ X2) != sK0)) )),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f8])).
% 1.61/1.30 thf(f8,plain,(
% 1.61/1.30 ! [X1 : $i > $i,X2 : $i] : ((X1 @ X2) != sK0)),
% 1.61/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7])).
% 1.61/1.30 thf(f7,plain,(
% 1.61/1.30 ? [X0 : $i] : ! [X1 : $i > $i,X2 : $i] : ((X1 @ X2) != X0) => ! [X2 : $i,X1 : $i > $i] : ((X1 @ X2) != sK0)),
% 1.61/1.30 introduced(definition,[],[choice_axiom])).
% 1.61/1.30 thf(f6,plain,(
% 1.61/1.30 ? [X0 : $i] : ! [X1 : $i > $i,X2 : $i] : ((X1 @ X2) != X0)),
% 1.61/1.30 inference(rectify,[status(thm)],[f5])).
% 1.61/1.30 thf(f5,plain,(
% 1.61/1.30 ? [X0 : $i] : ! [X2 : $i > $i,X1 : $i] : ((X2 @ X1) != X0)),
% 1.61/1.30 inference(ennf_transformation,[status(thm)],[f4])).
% 1.61/1.30 thf(f4,plain,(
% 1.61/1.30 ~! [X0 : $i] : ? [X2 : $i > $i,X1 : $i] : ((X2 @ X1) = X0)),
% 1.61/1.30 inference(rectify,[status(thm)],[f2])).
% 1.61/1.30 thf(f2,negated_conjecture,(
% 1.61/1.30 ~! [X0 : $i] : ? [X2 : $i,X1 : $i > $i] : ((X1 @ X2) = X0)),
% 1.61/1.30 inference(negated_conjecture,[status(cth)],[f1])).
% 1.61/1.30 thf(f1,conjecture,(
% 1.61/1.30 ! [X0 : $i] : ? [X2 : $i,X1 : $i > $i] : ((X1 @ X2) = X0)),
% 1.61/1.30 file('/export/starexec/sandbox/tmp/tmp.SjG4dn3XhK/DTF2THF_10544.p',cTHM139_pme)).
% 1.61/1.30 % SZS output end Proof for DTF2THF_10544
% 1.61/1.30 % (10823)------------------------------
% 1.61/1.30 % (10823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (10823)Termination reason: Refutation
% 1.61/1.30
% 1.61/1.30 % (10823)Memory used [KB]: 5373
% 1.61/1.30 % (10823)Time elapsed: 0.003 s
% 1.61/1.30 % (10823)Instructions burned: 1 (million)
% 1.61/1.30 % (10823)------------------------------
% 1.61/1.30 % (10823)------------------------------
% 1.61/1.30 % (10822)Success in time 0.019 s
%------------------------------------------------------------------------------