%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO206^5 : 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 : n015.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 09:53:39 AM UTC 2026
% Result : Theorem 1.64s 1.46s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 32 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 30 ( 13 ~; 10 |; 4 &)
% ( 1 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 78 ( 18 fml; 60 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 17 ( 11 !; 6 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_2,type,
sK0: $o > $o ).
tff(f14,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f12,f13]) ).
tff(f13,plain,
! [X0: $o] : ( sK0((X0)) != (X0) ),
inference(duplicate_literal_removal,[status(thm)],[f11]) ).
tff(f11,plain,
! [X0: $o] :
( ( sK0((X0)) != (X0) )
| ( sK0((X0)) != (X0) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
tff(f9,plain,
! [X0: $o] :
( ( ( sK0((X0)) != (X0) )
| ( sK0((X0)) != (X0) ) )
& ( ( sK0((X0)) = (X0) )
| ( sK0((X0)) = (X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8]) ).
tff(f8,plain,
! [X0: $o] :
( ? [X1: $o] :
( ( ( (X0) != (X1) )
| ( (X0) != (X1) ) )
& ( ( (X0) = (X1) )
| ( (X0) = (X1) ) ) )
=> ( ( ( sK0((X0)) != (X0) )
| ( sK0((X0)) != (X0) ) )
& ( ( sK0((X0)) = (X0) )
| ( sK0((X0)) = (X0) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
tff(f7,plain,
! [X0: $o] :
? [X1: $o] :
( ( ( (X0) != (X1) )
| ( (X0) != (X1) ) )
& ( ( (X0) = (X1) )
| ( (X0) = (X1) ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
tff(f6,plain,
! [X0: $o] :
? [X1: $o] :
( ( (X0) = (X1) )
<~> ( (X0) = (X1) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
tff(f5,plain,
~ ? [X0: $o] :
! [X1: $o] :
( ( (X0) = (X1) )
<=> ( (X0) = (X1) ) ),
inference(fool_elimination,[status(thm)],[f2]) ).
tff(f2,negated_conjecture,
~ ? [X0: $o] :
! [X1: $o] :
( ( (X0) = (X1) )
= ( (X0) = (X1) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f1,conjecture,
? [X0: $o] :
! [X1: $o] :
( ( (X0) = (X1) )
= ( (X0) = (X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.mx54AnOW9K/DTF2THF_23110.p',cCT265) ).
tff(f12,plain,
! [X0: $o] : ( sK0((X0)) = (X0) ),
inference(duplicate_literal_removal,[status(thm)],[f10]) ).
tff(f10,plain,
! [X0: $o] :
( ( sK0((X0)) = (X0) )
| ( sK0((X0)) = (X0) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO206^5 : 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 : n015.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 14:26:01 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
% 0.33/0.50 ---- Original DTF file ---
% 0.33/0.50 thf(spec,logic,$$dhol).
% 0.33/0.50 %------------------------------------------------------------------------------
% 0.33/0.50 % File : SYO206^5 : TPTP v9.2.1. Released v4.0.0.
% 0.33/0.50 % Domain : Syntactic
% 0.33/0.50 % Problem : TPS problem CT265
% 0.33/0.50 % Version : Especial.
% 0.33/0.50 % English :
% 0.33/0.50
% 0.33/0.50 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.33/0.50 % Source : [Bro09]
% 0.33/0.50 % Names : tps_0172 [Bro09]
% 0.33/0.50 % : CT265 [TPS]
% 0.33/0.50 % : CT23A [TPS]
% 0.33/0.50
% 0.33/0.50 % Status : Theorem
% 0.33/0.50 % Rating : 0.00 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 v4.1.0, 0.00 v4.0.0
% 0.33/0.50 % Syntax : Number of formulae : 1 ( 1 unt; 0 typ; 0 def)
% 0.33/0.50 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.33/0.50 % Maximal formula atoms : 1 ( 3 avg)
% 0.33/0.50 % Number of connectives : 0 ( 0 ~; 0 |; 0 &; 0 @)
% 0.33/0.50 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.33/0.50 % Maximal formula depth : 3 ( 3 avg)
% 0.33/0.50 % Number of types : 1 ( 0 usr)
% 0.33/0.50 % Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 0.33/0.50 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.33/0.50 % Number of variables : 2 ( 0 ^; 1 !; 1 ?; 2 :)
% 0.33/0.50 % SPC : TH0_THM_EQU_NAR
% 0.33/0.50
% 0.33/0.50 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.33/0.50 % project in the Department of Mathematical Sciences at Carnegie
% 0.33/0.50 % Mellon University. Distributed under the Creative Commons copyleft
% 0.33/0.50 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.33/0.50 %------------------------------------------------------------------------------
% 0.33/0.50 thf(cCT265,conjecture,
% 0.33/0.50 ? [Xx: $o] :
% 0.33/0.50 ! [Xy: $o] :
% 0.33/0.50 ( ( Xx = Xy )
% 0.33/0.50 = ( Xy = Xx ) ) ).
% 0.33/0.50
% 0.33/0.50 %------------------------------------------------------------------------------
% 0.33/0.50 ------------------------
% 1.64/1.43 ---- Embedded in THF ---
% 1.64/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.64/1.43 %%% Generated on Tue Feb 24 14:26:02 EST 2026
% 1.64/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 1.64/1.43 %%% Logic specification used:
% 1.64/1.43 %%% thf(spec, logic, $$dhol).
% 1.64/1.43
% 1.64/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.mx54AnOW9K/DTF2DTF23110.p
% See solution above
% 1.64/1.43 ------------------------
% 1.64/1.44 ---- Cleaned THF ---
% 1.64/1.44 thf(cCT265,conjecture,
% 1.64/1.44 ? [Xx: $o] :
% 1.64/1.44 ! [Xy: $o] :
% 1.64/1.44 ( ( Xx = Xy )
% 1.64/1.44 = ( Xy = Xx ) ) ).
% 1.64/1.44 ------------------------
% 1.64/1.46 % (23224)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23110 for (3000ds/183Mi)
% 1.64/1.46 % (23225)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_23110 for (3000ds/4Mi)
% 1.64/1.46 % (23226)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_23110 for (3000ds/27Mi)
% 1.64/1.46 % (23228)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_23110 for (3000ds/2Mi)
% 1.64/1.46 % (23227)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23110 for (3000ds/2Mi)
% 1.64/1.46 % (23229)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_23110 for (3000ds/275Mi)
% 1.64/1.46 % (23230)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23110 for (3000ds/18Mi)
% 1.64/1.46 % (23224)First to succeed.
% 1.64/1.46 % (23225)Also succeeded, but the first one will report.
% 1.64/1.46 % (23226)Also succeeded, but the first one will report.
% 1.64/1.46 % (23224)Refutation found. Thanks to Tanya!
% 1.64/1.46 % SZS status Theorem for DTF2THF_23110
% 1.64/1.46 % SZS output start Proof for DTF2THF_23110
% 1.64/1.46 tff(func_def_2, type, sK0: ($o) > $o).
% 1.64/1.46 tff(f14,plain,(
% 1.64/1.46 $false),
% 1.64/1.46 inference(subsumption_resolution,[status(thm)],[f12,f13])).
% 1.64/1.46 tff(f13,plain,(
% 1.64/1.46 ( ! [X0 : $o] : ((sK0(X0) != X0)) )),
% 1.64/1.46 inference(duplicate_literal_removal,[status(thm)],[f11])).
% 1.64/1.46 tff(f11,plain,(
% 1.64/1.46 ( ! [X0 : $o] : ((sK0(X0) != X0) | (sK0(X0) != X0)) )),
% 1.64/1.46 inference(cnf_transformation,[status(thm)],[f9])).
% 1.64/1.46 tff(f9,plain,(
% 1.64/1.46 ! [X0 : $o] : (((sK0(X0) != X0) | (sK0(X0) != X0)) & ((sK0(X0) = X0) | (sK0(X0) = X0)))),
% 1.64/1.46 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8])).
% 1.64/1.46 tff(f8,plain,(
% 1.64/1.46 ! [X0 : $o] : (? [X1 : $o] : (((X0 != X1) | (X0 != X1)) & ((X0 = X1) | (X0 = X1))) => (((sK0(X0) != X0) | (sK0(X0) != X0)) & ((sK0(X0) = X0) | (sK0(X0) = X0))))),
% 1.64/1.46 introduced(definition,[],[choice_axiom])).
% 1.64/1.46 tff(f7,plain,(
% 1.64/1.46 ! [X0 : $o] : ? [X1 : $o] : (((X0 != X1) | (X0 != X1)) & ((X0 = X1) | (X0 = X1)))),
% 1.64/1.46 inference(nnf_transformation,[status(thm)],[f6])).
% 1.64/1.46 tff(f6,plain,(
% 1.64/1.46 ! [X0 : $o] : ? [X1 : $o] : ((X0 = X1) <~> (X0 = X1))),
% 1.64/1.46 inference(ennf_transformation,[status(thm)],[f5])).
% 1.64/1.46 tff(f5,plain,(
% 1.64/1.46 ~? [X0 : $o] : ! [X1 : $o] : ((X0 = X1) <=> (X0 = X1))),
% 1.64/1.46 inference(fool_elimination,[status(thm)],[f2])).
% 1.64/1.46 tff(f2,negated_conjecture,(
% 1.64/1.46 ~? [X0 : $o] : ! [X1 : $o] : ((X0 = X1) = (X0 = X1))),
% 1.64/1.46 inference(negated_conjecture,[status(cth)],[f1])).
% 1.64/1.46 tff(f1,conjecture,(
% 1.64/1.46 ? [X0 : $o] : ! [X1 : $o] : ((X0 = X1) = (X0 = X1))),
% 1.64/1.46 file('/export/starexec/sandbox/tmp/tmp.mx54AnOW9K/DTF2THF_23110.p',cCT265)).
% 1.64/1.46 tff(f12,plain,(
% 1.64/1.46 ( ! [X0 : $o] : ((sK0(X0) = X0)) )),
% 1.64/1.46 inference(duplicate_literal_removal,[status(thm)],[f10])).
% 1.64/1.46 tff(f10,plain,(
% 1.64/1.46 ( ! [X0 : $o] : ((sK0(X0) = X0) | (sK0(X0) = X0)) )),
% 1.64/1.46 inference(cnf_transformation,[status(thm)],[f9])).
% 1.64/1.46 % SZS output end Proof for DTF2THF_23110
% 1.64/1.46 % (23224)------------------------------
% 1.64/1.46 % (23224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.46 % (23224)Termination reason: Refutation
% 1.64/1.46
% 1.64/1.46 % (23224)Memory used [KB]: 5373
% 1.64/1.46 % (23224)Time elapsed: 0.002 s
% 1.64/1.46 % (23224)Instructions burned: 1 (million)
% 1.64/1.46 % (23224)------------------------------
% 1.64/1.46 % (23224)------------------------------
% 1.64/1.46 % (23223)Success in time 0.017 s
%------------------------------------------------------------------------------