%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU928^5 : 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 : n003.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 09:37:46 AM UTC 2026
% Result : Theorem 1.80s 1.53s
% Output : Refutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 46 equ; 0 cnn)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 119 ( 18 ~; 8 |; 12 &; 70 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 0 ^; 29 !; 13 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_3,type,
sK0: $i > $i ).
thf(f23,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f22,f10]) ).
thf(f10,plain,
sK2 != sK1,
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ( ( sK0 @ X1 )
!= ( sK0 @ X2 ) ) )
& ( ( sK0 @ ( sK0 @ sK2 ) )
= ( sK0 @ ( sK0 @ sK1 ) ) )
& ( sK2 != sK1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f8,f7]) ).
thf(f7,plain,
( ? [X0: $i > $i] :
( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ( ( X0 @ X1 )
!= ( X0 @ X2 ) ) )
& ? [X3: $i,X4: $i] :
( ( ( X0 @ ( X0 @ X3 ) )
= ( X0 @ ( X0 @ X4 ) ) )
& ( X3 != X4 ) ) )
=> ( ! [X2: $i,X1: $i] :
( ( X1 = X2 )
| ( ( sK0 @ X1 )
!= ( sK0 @ X2 ) ) )
& ? [X4: $i,X3: $i] :
( ( ( sK0 @ ( sK0 @ X3 ) )
= ( sK0 @ ( sK0 @ X4 ) ) )
& ( X3 != X4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ? [X4: $i,X3: $i] :
( ( ( sK0 @ ( sK0 @ X3 ) )
= ( sK0 @ ( sK0 @ X4 ) ) )
& ( X3 != X4 ) )
=> ( ( ( sK0 @ ( sK0 @ sK2 ) )
= ( sK0 @ ( sK0 @ sK1 ) ) )
& ( sK2 != sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: $i > $i] :
( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
| ( ( X0 @ X1 )
!= ( X0 @ X2 ) ) )
& ? [X3: $i,X4: $i] :
( ( ( X0 @ ( X0 @ X3 ) )
= ( X0 @ ( X0 @ X4 ) ) )
& ( X3 != X4 ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
? [X0: $i > $i] :
( ! [X2: $i,X1: $i] :
( ( X1 = X2 )
| ( ( X0 @ X1 )
!= ( X0 @ X2 ) ) )
& ? [X4: $i,X3: $i] :
( ( ( X0 @ ( X0 @ X3 ) )
= ( X0 @ ( X0 @ X4 ) ) )
& ( X3 != X4 ) ) ),
inference(ennf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i > $i] :
( ! [X2: $i,X1: $i] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X4: $i,X3: $i] :
( ( ( X0 @ ( X0 @ X3 ) )
= ( X0 @ ( X0 @ X4 ) ) )
=> ( X3 = X4 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: $i > $i] :
( ! [X2: $i,X1: $i] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: $i,X2: $i] :
( ( ( X0 @ ( X0 @ X1 ) )
= ( X0 @ ( X0 @ X2 ) ) )
=> ( X1 = X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: $i > $i] :
( ! [X2: $i,X1: $i] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) )
=> ! [X1: $i,X2: $i] :
( ( ( X0 @ ( X0 @ X1 ) )
= ( X0 @ ( X0 @ X2 ) ) )
=> ( X1 = X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zeBJG3aBea/DTF2THF_13757.p',cTHM48A_pme) ).
thf(f22,plain,
sK2 = sK1,
inference(equality_resolution,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $i] :
( ( ( sK0 @ sK1 )
!= ( sK0 @ X0 ) )
| ( sK2 = X0 ) ),
inference(superposition,[status(thm)],[f12,f17]) ).
thf(f17,plain,
( ( sK0 @ sK2 )
= ( sK0 @ sK1 ) ),
inference(equality_resolution,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $i] :
( ( ( sK0 @ X0 )
!= ( sK0 @ ( sK0 @ sK1 ) ) )
| ( ( sK0 @ sK2 )
= X0 ) ),
inference(superposition,[status(thm)],[f12,f11]) ).
thf(f11,plain,
( ( sK0 @ ( sK0 @ sK2 ) )
= ( sK0 @ ( sK0 @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f12,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ X1 )
!= ( sK0 @ X2 ) )
| ( X1 = X2 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU928^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n003.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:37:10 EST 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.47 ---- Original DTF file ---
% 0.21/0.47 thf(spec,logic,$$dhol).
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 % File : SEU928^5 : TPTP v9.2.1. Released v4.0.0.
% 0.21/0.47 % Domain : Set Theory (Functions)
% 0.21/0.47 % Problem : TPS problem THM48A
% 0.21/0.47 % Version : Especial.
% 0.21/0.47 % English :
% 0.21/0.47
% 0.21/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.47 % Source : [Bro09]
% 0.21/0.47 % Names : tps_0244 [Bro09]
% 0.21/0.47 % : THM48A [TPS]
% 0.21/0.47
% 0.21/0.47 % Status : Theorem
% 0.21/0.47 % Rating : 0.00 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.21/0.47 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.21/0.47 % Number of atoms : 4 ( 4 equ; 0 cnn)
% 0.21/0.47 % Maximal formula atoms : 4 ( 4 avg)
% 0.21/0.47 % Number of connectives : 9 ( 0 ~; 0 |; 0 &; 6 @)
% 0.21/0.47 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.21/0.47 % Maximal formula depth : 6 ( 6 avg)
% 0.21/0.47 % Number of types : 1 ( 0 usr)
% 0.21/0.47 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.21/0.47 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.21/0.47 % Number of variables : 5 ( 0 ^; 5 !; 0 ?; 5 :)
% 0.21/0.47 % SPC : TH0_THM_EQU_NAR
% 0.21/0.47
% 0.21/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.21/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.21/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.21/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.21/0.47 % : Polymorphic definitions expanded.
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 thf(cTHM48A_pme,conjecture,
% 0.21/0.47 ! [F: $i > $i] :
% 0.21/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.21/0.47 ( ( ( F @ Xx )
% 0.21/0.47 = ( F @ Xy ) )
% 0.21/0.47 => ( Xx = Xy ) )
% 0.21/0.47 => ! [Xx: $i,Xy: $i] :
% 0.21/0.47 ( ( ( F @ ( F @ Xx ) )
% 0.21/0.47 = ( F @ ( F @ Xy ) ) )
% 0.21/0.47 => ( Xx = Xy ) ) ) ).
% 0.21/0.47
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 ------------------------
% 1.61/1.49 ---- Embedded in THF ---
% 1.61/1.49 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.61/1.49 %%% Generated on Tue Feb 24 12:37:12 EST 2026
% 1.61/1.49 %%% using '$$dhol' embedding, version 1.3.0.
% 1.61/1.49 %%% Logic specification used:
% 1.61/1.49 %%% thf(spec, logic, $$dhol).
% 1.61/1.49
% 1.61/1.49 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.zeBJG3aBea/DTF2DTF13757.p
% See solution above
% 1.61/1.49 ------------------------
% 1.80/1.50 ---- Cleaned THF ---
% 1.80/1.50 thf(cTHM48A_pme,conjecture,
% 1.80/1.50 ! [F: $i > $i] :
% 1.80/1.50 ( ! [Xx: $i,Xy: $i] :
% 1.80/1.50 ( ( ( F @ Xx )
% 1.80/1.50 = ( F @ Xy ) )
% 1.80/1.50 => ( Xx = Xy ) )
% 1.80/1.50 => ! [Xx: $i,Xy: $i] :
% 1.80/1.50 ( ( ( F @ ( F @ Xx ) )
% 1.80/1.50 = ( F @ ( F @ Xy ) ) )
% 1.80/1.50 => ( Xx = Xy ) ) ) ).
% 1.80/1.50 ------------------------
% 1.80/1.52 % (13871)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_13757 for (2999ds/4Mi)
% 1.80/1.52 % (13873)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13757 for (2999ds/2Mi)
% 1.80/1.52 % (13876)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13757 for (2999ds/18Mi)
% 1.80/1.52 % (13874)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_13757 for (2999ds/2Mi)
% 1.80/1.52 % (13872)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_13757 for (2999ds/27Mi)
% 1.80/1.52 % (13870)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13757 for (2999ds/183Mi)
% 1.80/1.52 % (13875)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_13757 for (2999ds/275Mi)
% 1.80/1.52 % (13874)Instruction limit reached!
% 1.80/1.52 % (13874)------------------------------
% 1.80/1.52 % (13874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.52 % (13874)Termination reason: Unknown
% 1.80/1.52 % (13874)Termination phase: Saturation
% 1.80/1.52
% 1.80/1.52 % (13874)Memory used [KB]: 895
% 1.80/1.52 % (13874)Time elapsed: 0.003 s
% 1.80/1.52 % (13874)Instructions burned: 2 (million)
% 1.80/1.52 % (13874)------------------------------
% 1.80/1.52 % (13874)------------------------------
% 1.80/1.52 % (13873)Instruction limit reached!
% 1.80/1.52 % (13873)------------------------------
% 1.80/1.52 % (13873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.52 % (13873)Termination reason: Unknown
% 1.80/1.52 % (13873)Termination phase: Saturation
% 1.80/1.52
% 1.80/1.52 % (13873)Memory used [KB]: 5500
% 1.80/1.52 % (13873)Time elapsed: 0.004 s
% 1.80/1.52 % (13873)Instructions burned: 2 (million)
% 1.80/1.52 % (13873)------------------------------
% 1.80/1.52 % (13873)------------------------------
% 1.80/1.52 % (13870)First to succeed.
% 1.80/1.52 % (13875)Also succeeded, but the first one will report.
% 1.80/1.52 % (13871)Also succeeded, but the first one will report.
% 1.80/1.53 % (13870)Refutation found. Thanks to Tanya!
% 1.80/1.53 % SZS status Theorem for DTF2THF_13757
% 1.80/1.53 % SZS output start Proof for DTF2THF_13757
% 1.80/1.53 thf(func_def_3, type, sK0: $i > $i).
% 1.80/1.53 thf(f23,plain,(
% 1.80/1.53 $false),
% 1.80/1.53 inference(subsumption_resolution,[status(thm)],[f22,f10])).
% 1.80/1.53 thf(f10,plain,(
% 1.80/1.53 (sK2 != sK1)),
% 1.80/1.53 inference(cnf_transformation,[status(thm)],[f9])).
% 1.80/1.53 thf(f9,plain,(
% 1.80/1.53 ! [X1 : $i,X2 : $i] : ((X1 = X2) | ((sK0 @ X1) != (sK0 @ X2))) & (((sK0 @ (sK0 @ sK2)) = (sK0 @ (sK0 @ sK1))) & (sK2 != sK1))),
% 1.80/1.53 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f6,f8,f7])).
% 1.80/1.53 thf(f7,plain,(
% 1.80/1.53 ? [X0 : $i > $i] : (! [X1 : $i,X2 : $i] : ((X1 = X2) | ((X0 @ X1) != (X0 @ X2))) & ? [X3 : $i,X4 : $i] : (((X0 @ (X0 @ X3)) = (X0 @ (X0 @ X4))) & (X3 != X4))) => (! [X2 : $i,X1 : $i] : ((X1 = X2) | ((sK0 @ X1) != (sK0 @ X2))) & ? [X4 : $i,X3 : $i] : (((sK0 @ (sK0 @ X3)) = (sK0 @ (sK0 @ X4))) & (X3 != X4)))),
% 1.80/1.53 introduced(definition,[],[choice_axiom])).
% 1.80/1.53 thf(f8,plain,(
% 1.80/1.53 ? [X4 : $i,X3 : $i] : (((sK0 @ (sK0 @ X3)) = (sK0 @ (sK0 @ X4))) & (X3 != X4)) => (((sK0 @ (sK0 @ sK2)) = (sK0 @ (sK0 @ sK1))) & (sK2 != sK1))),
% 1.80/1.53 introduced(definition,[],[choice_axiom])).
% 1.80/1.53 thf(f6,plain,(
% 1.80/1.53 ? [X0 : $i > $i] : (! [X1 : $i,X2 : $i] : ((X1 = X2) | ((X0 @ X1) != (X0 @ X2))) & ? [X3 : $i,X4 : $i] : (((X0 @ (X0 @ X3)) = (X0 @ (X0 @ X4))) & (X3 != X4)))),
% 1.80/1.53 inference(rectify,[status(thm)],[f5])).
% 1.80/1.53 thf(f5,plain,(
% 1.80/1.53 ? [X0 : $i > $i] : (! [X2 : $i,X1 : $i] : ((X1 = X2) | ((X0 @ X1) != (X0 @ X2))) & ? [X4 : $i,X3 : $i] : (((X0 @ (X0 @ X3)) = (X0 @ (X0 @ X4))) & (X3 != X4)))),
% 1.80/1.53 inference(ennf_transformation,[status(thm)],[f4])).
% 1.80/1.53 thf(f4,plain,(
% 1.80/1.53 ~! [X0 : $i > $i] : (! [X2 : $i,X1 : $i] : (((X0 @ X1) = (X0 @ X2)) => (X1 = X2)) => ! [X4 : $i,X3 : $i] : (((X0 @ (X0 @ X3)) = (X0 @ (X0 @ X4))) => (X3 = X4)))),
% 1.80/1.53 inference(rectify,[status(thm)],[f2])).
% 1.80/1.53 thf(f2,negated_conjecture,(
% 1.80/1.53 ~! [X0 : $i > $i] : (! [X2 : $i,X1 : $i] : (((X0 @ X1) = (X0 @ X2)) => (X1 = X2)) => ! [X1 : $i,X2 : $i] : (((X0 @ (X0 @ X1)) = (X0 @ (X0 @ X2))) => (X1 = X2)))),
% 1.80/1.53 inference(negated_conjecture,[status(cth)],[f1])).
% 1.80/1.53 thf(f1,conjecture,(
% 1.80/1.53 ! [X0 : $i > $i] : (! [X2 : $i,X1 : $i] : (((X0 @ X1) = (X0 @ X2)) => (X1 = X2)) => ! [X1 : $i,X2 : $i] : (((X0 @ (X0 @ X1)) = (X0 @ (X0 @ X2))) => (X1 = X2)))),
% 1.80/1.53 file('/export/starexec/sandbox/tmp/tmp.zeBJG3aBea/DTF2THF_13757.p',cTHM48A_pme)).
% 1.80/1.53 thf(f22,plain,(
% 1.80/1.53 (sK2 = sK1)),
% 1.80/1.53 inference(equality_resolution,[status(thm)],[f18])).
% 1.80/1.53 thf(f18,plain,(
% 1.80/1.53 ( ! [X0 : $i] : (((sK0 @ sK1) != (sK0 @ X0)) | (sK2 = X0)) )),
% 1.80/1.53 inference(superposition,[status(thm)],[f12,f17])).
% 1.80/1.53 thf(f17,plain,(
% 1.80/1.53 ((sK0 @ sK2) = (sK0 @ sK1))),
% 1.80/1.53 inference(equality_resolution,[status(thm)],[f15])).
% 1.80/1.53 thf(f15,plain,(
% 1.80/1.53 ( ! [X0 : $i] : (((sK0 @ X0) != (sK0 @ (sK0 @ sK1))) | ((sK0 @ sK2) = X0)) )),
% 1.80/1.53 inference(superposition,[status(thm)],[f12,f11])).
% 1.80/1.53 thf(f11,plain,(
% 1.80/1.53 ((sK0 @ (sK0 @ sK2)) = (sK0 @ (sK0 @ sK1)))),
% 1.80/1.53 inference(cnf_transformation,[status(thm)],[f9])).
% 1.80/1.53 thf(f12,plain,(
% 1.80/1.53 ( ! [X2 : $i,X1 : $i] : (((sK0 @ X1) != (sK0 @ X2)) | (X1 = X2)) )),
% 1.80/1.53 inference(cnf_transformation,[status(thm)],[f9])).
% 1.80/1.53 % SZS output end Proof for DTF2THF_13757
% 1.80/1.53 % (13870)------------------------------
% 1.80/1.53 % (13870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.53 % (13870)Termination reason: Refutation
% 1.80/1.53
% 1.80/1.53 % (13870)Memory used [KB]: 5500
% 1.80/1.53 % (13870)Time elapsed: 0.005 s
% 1.80/1.53 % (13870)Instructions burned: 2 (million)
% 1.80/1.53 % (13870)------------------------------
% 1.80/1.53 % (13870)------------------------------
% 1.80/1.53 % (13869)Success in time 0.019 s
%------------------------------------------------------------------------------