%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO202^5 : 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 : n017.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 1.52s 1.35s
% Output : Refutation 1.52s
% 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 : 69 ( 32 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 46 ( 17 ~; 0 |; 8 &; 20 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 1 usr; 2 con; 0-2 aty)
% Number of variables : 6 ( 0 ^; 0 !; 6 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_4,type,
sK0: $o > $o ).
thf(f13,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f11,f12]) ).
thf(f12,plain,
( ( sK0 @ $true )
= $true ),
inference(boolean_simplification,[status(thm)],[f9]) ).
thf(f9,plain,
( $true
= ( sK0 @ ( sK0 = sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( $true
!= ( sK0 @ ( sK0 = sK0 ) ) )
& ( $true
= ( sK0 @ ( sK0 = sK0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: $o > $o] :
( ( $true
!= ( X0 @ ( X0 = X0 ) ) )
& ( $true
= ( X0 @ ( X0 = X0 ) ) ) )
=> ( ( $true
!= ( sK0 @ ( sK0 = sK0 ) ) )
& ( $true
= ( sK0 @ ( sK0 = sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: $o > $o] :
( ( $true
!= ( X0 @ ( X0 = X0 ) ) )
& ( $true
= ( X0 @ ( X0 = X0 ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ~ ? [X0: $o > $o] :
( ( $true
!= ( X0 @ ( X0 = X0 ) ) )
& ( $true
= ( X0 @ ( X0 = X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ~ ? [X0: $o > $o] :
( ~ ( X0 @ ( X0 = X0 ) )
& ( X0 @ ( X0 = X0 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ~ ? [X0: $o > $o] :
( ~ ( X0 @ ( X0 = X0 ) )
& ( X0 @ ( X0 = X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
~ ? [X0: $o > $o] :
( ~ ( X0 @ ( X0 = X0 ) )
& ( X0 @ ( X0 = X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zfjUbRMuhB/DTF2THF_24666.p',cCT22) ).
thf(f11,plain,
( ( sK0 @ $true )
!= $true ),
inference(boolean_simplification,[status(thm)],[f10]) ).
thf(f10,plain,
( $true
!= ( sK0 @ ( sK0 = sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO202^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.30 % Computer : n017.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Feb 24 14:25:11 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.40 ---- Original DTF file ---
% 0.16/0.40 thf(spec,logic,$$dhol).
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 % File : SYO202^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.40 % Domain : Syntactic
% 0.16/0.40 % Problem : TPS problem CT22
% 0.16/0.40 % Version : Especial.
% 0.16/0.40 % English :
% 0.16/0.40
% 0.16/0.40 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.40 % Source : [Bro09]
% 0.16/0.40 % Names : tps_0066 [Bro09]
% 0.16/0.40 % : CT22 [TPS]
% 0.16/0.40
% 0.16/0.40 % Status : Theorem
% 0.16/0.40 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.15 v8.1.0, 0.00 v6.2.0, 0.14 v6.1.0, 0.00 v6.0.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.16/0.40 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.16/0.40 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.16/0.40 % Maximal formula atoms : 2 ( 2 avg)
% 0.16/0.40 % Number of connectives : 5 ( 2 ~; 0 |; 1 &; 2 @)
% 0.16/0.40 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.16/0.40 % Maximal formula depth : 6 ( 6 avg)
% 0.16/0.40 % Number of types : 1 ( 0 usr)
% 0.16/0.40 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.16/0.40 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.16/0.40 % Number of variables : 1 ( 0 ^; 0 !; 1 ?; 1 :)
% 0.16/0.40 % SPC : TH0_THM_EQU_NAR
% 0.16/0.40
% 0.16/0.40 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.40 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.40 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.40 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 thf(cCT22,conjecture,
% 0.16/0.40 ~ ? [Xp: $o > $o] :
% 0.16/0.40 ( ( Xp @ ( Xp = Xp ) )
% 0.16/0.40 & ~ ( Xp @ ( Xp = Xp ) ) ) ).
% 0.16/0.40
% 0.16/0.40 %------------------------------------------------------------------------------
% 0.16/0.40 ------------------------
% 1.52/1.32 ---- Embedded in THF ---
% 1.52/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.52/1.32 %%% Generated on Tue Feb 24 14:25:11 EST 2026
% 1.52/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.52/1.32 %%% Logic specification used:
% 1.52/1.32 %%% thf(spec, logic, $$dhol).
% 1.52/1.32
% 1.52/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.zfjUbRMuhB/DTF2DTF24666.p
% See solution above
% 1.52/1.32 ------------------------
% 1.52/1.33 ---- Cleaned THF ---
% 1.52/1.33 thf(cCT22,conjecture,
% 1.52/1.33 ~ ? [Xp: $o > $o] :
% 1.52/1.33 ( ( Xp @ ( Xp = Xp ) )
% 1.52/1.33 & ~ ( Xp @ ( Xp = Xp ) ) ) ).
% 1.52/1.33 ------------------------
% 1.52/1.35 % (24766)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_24666 for (3000ds/2Mi)
% 1.52/1.35 % (24763)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_24666 for (3000ds/183Mi)
% 1.52/1.35 % (24764)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_24666 for (3000ds/4Mi)
% 1.52/1.35 % (24769)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_24666 for (3000ds/18Mi)
% 1.52/1.35 % (24768)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_24666 for (3000ds/275Mi)
% 1.52/1.35 % (24765)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_24666 for (3000ds/27Mi)
% 1.52/1.35 % (24767)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_24666 for (3000ds/2Mi)
% 1.52/1.35 % (24768)First to succeed.
% 1.52/1.35 % (24763)Also succeeded, but the first one will report.
% 1.52/1.35 % (24764)Also succeeded, but the first one will report.
% 1.52/1.35 % (24768)Refutation found. Thanks to Tanya!
% 1.52/1.35 % SZS status Theorem for DTF2THF_24666
% 1.52/1.35 % SZS output start Proof for DTF2THF_24666
% 1.52/1.35 thf(func_def_4, type, sK0: $o > $o).
% 1.52/1.35 thf(f13,plain,(
% 1.52/1.35 $false),
% 1.52/1.35 inference(subsumption_resolution,[status(thm)],[f11,f12])).
% 1.52/1.35 thf(f12,plain,(
% 1.52/1.35 ((sK0 @ $true) = $true)),
% 1.52/1.35 inference(boolean_simplification,[status(thm)],[f9])).
% 1.52/1.35 thf(f9,plain,(
% 1.52/1.35 ($true = (sK0 @ (sK0 = sK0)))),
% 1.52/1.35 inference(cnf_transformation,[status(thm)],[f8])).
% 1.52/1.35 thf(f8,plain,(
% 1.52/1.35 ($true != (sK0 @ (sK0 = sK0))) & ($true = (sK0 @ (sK0 = sK0)))),
% 1.52/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7])).
% 1.52/1.35 thf(f7,plain,(
% 1.52/1.35 ? [X0 : $o > $o] : (($true != (X0 @ (X0 = X0))) & ($true = (X0 @ (X0 = X0)))) => (($true != (sK0 @ (sK0 = sK0))) & ($true = (sK0 @ (sK0 = sK0))))),
% 1.52/1.35 introduced(definition,[],[choice_axiom])).
% 1.52/1.35 thf(f6,plain,(
% 1.52/1.35 ? [X0 : $o > $o] : (($true != (X0 @ (X0 = X0))) & ($true = (X0 @ (X0 = X0))))),
% 1.52/1.35 inference(flattening,[status(thm)],[f5])).
% 1.52/1.35 thf(f5,plain,(
% 1.52/1.35 ~~? [X0 : $o > $o] : (~($true = (X0 @ (X0 = X0))) & ($true = (X0 @ (X0 = X0))))),
% 1.52/1.35 inference(fool_elimination,[status(thm)],[f4])).
% 1.52/1.35 thf(f4,plain,(
% 1.52/1.35 ~~? [X0 : $o > $o] : (~(X0 @ (X0 = X0)) & (X0 @ (X0 = X0)))),
% 1.52/1.35 inference(rectify,[status(thm)],[f2])).
% 1.52/1.35 thf(f2,negated_conjecture,(
% 1.52/1.35 ~~? [X0 : $o > $o] : (~(X0 @ (X0 = X0)) & (X0 @ (X0 = X0)))),
% 1.52/1.35 inference(negated_conjecture,[status(cth)],[f1])).
% 1.52/1.35 thf(f1,conjecture,(
% 1.52/1.35 ~? [X0 : $o > $o] : (~(X0 @ (X0 = X0)) & (X0 @ (X0 = X0)))),
% 1.52/1.35 file('/export/starexec/sandbox/tmp/tmp.zfjUbRMuhB/DTF2THF_24666.p',cCT22)).
% 1.52/1.35 thf(f11,plain,(
% 1.52/1.35 ((sK0 @ $true) != $true)),
% 1.52/1.35 inference(boolean_simplification,[status(thm)],[f10])).
% 1.52/1.35 thf(f10,plain,(
% 1.52/1.35 ($true != (sK0 @ (sK0 = sK0)))),
% 1.52/1.35 inference(cnf_transformation,[status(thm)],[f8])).
% 1.52/1.35 % SZS output end Proof for DTF2THF_24666
% 1.52/1.35 % (24768)------------------------------
% 1.52/1.35 % (24768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.35 % (24768)Termination reason: Refutation
% 1.52/1.35
% 1.52/1.35 % (24768)Memory used [KB]: 5373
% 1.52/1.35 % (24768)Time elapsed: 0.003 s
% 1.52/1.35 % (24768)Instructions burned: 1 (million)
% 1.52/1.35 % (24768)------------------------------
% 1.52/1.35 % (24768)------------------------------
% 1.52/1.35 % (24762)Success in time 0.018 s
%------------------------------------------------------------------------------