%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO282^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n024.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 09:53:51 AM UTC 2026
% Result : Theorem 1.03s 0.91s
% Output : Refutation 1.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 37 ( 14 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 38 ( 8 ~; 0 |; 4 &; 20 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 0 ^; 9 !; 14 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
b: $tType ).
thf(func_def_0,type,
b: $tType ).
thf(func_def_4,type,
sK0: b > $o ).
thf(func_def_5,type,
sK1: b ).
thf(f12,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f10,f11]) ).
thf(f11,plain,
! [X1: b] :
( $true
!= ( sK0 @ X1 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X1: b] :
( ( $true
!= ( sK0 @ X1 ) )
& ( $true
= ( sK0 @ sK1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7]) ).
thf(f7,plain,
( ? [X0: b > $o] :
! [X1: b] :
( ( ( X0 @ X1 )
!= $true )
& ? [X2: b] :
( ( X0 @ X2 )
= $true ) )
=> ! [X1: b] :
( ( $true
!= ( sK0 @ X1 ) )
& ? [X2: b] :
( $true
= ( sK0 @ X2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ? [X2: b] :
( $true
= ( sK0 @ X2 ) )
=> ( $true
= ( sK0 @ sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: b > $o] :
! [X1: b] :
( ( ( X0 @ X1 )
!= $true )
& ? [X2: b] :
( ( X0 @ X2 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: b > $o] :
? [X1: b] :
( ? [X2: b] :
( ( X0 @ X2 )
= $true )
=> ( ( X0 @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: b > $o] :
? [X1: b] :
( ? [X2: b] : ( X0 @ X2 )
=> ( X0 @ X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: b > $o] :
? [X1: b] :
( ? [X2: b] : ( X0 @ X2 )
=> ( X0 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: b > $o] :
? [X1: b] :
( ? [X2: b] : ( X0 @ X2 )
=> ( X0 @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.kDXdtsRDl1/DTF2THF_7657.p',cL51) ).
thf(f10,plain,
( $true
= ( sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SYO282^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.25 % Computer : n024.cluster.edu
% 0.08/0.25 % Model : x86_64 x86_64
% 0.08/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.25 % Memory : 8042.1875MB
% 0.08/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.25 % CPULimit : 300
% 0.08/0.25 % WCLimit : 300
% 0.08/0.25 % DateTime : Tue Feb 24 09:27:10 EST 2026
% 0.08/0.25 % CPUTime :
% 0.08/0.25 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.31 ---- Original DTF file ---
% 0.08/0.31 thf(spec,logic,$$dhol).
% 0.08/0.31 %------------------------------------------------------------------------------
% 0.08/0.31 % File : SYO282^5 : TPTP v9.2.1. Released v4.0.0.
% 0.08/0.31 % Domain : Syntactic
% 0.08/0.31 % Problem : TPS problem from BASIC-HO-THMS
% 0.08/0.31 % Version : Especial.
% 0.08/0.31 % English :
% 0.08/0.31
% 0.08/0.31 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.08/0.31 % Source : [Bro09]
% 0.08/0.31 % Names : tps_0665 [Bro09]
% 0.08/0.31
% 0.08/0.31 % Status : Theorem
% 0.08/0.31 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.0.0, 0.00 v4.0.0
% 0.08/0.31 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.08/0.31 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.08/0.31 % Maximal formula atoms : 0 ( 0 avg)
% 0.08/0.31 % Number of connectives : 3 ( 0 ~; 0 |; 0 &; 2 @)
% 0.08/0.31 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.08/0.31 % Maximal formula depth : 6 ( 6 avg)
% 0.08/0.31 % Number of types : 2 ( 1 usr)
% 0.08/0.31 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.08/0.31 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.08/0.31 % Number of variables : 3 ( 0 ^; 1 !; 2 ?; 3 :)
% 0.08/0.31 % SPC : TH0_THM_NEQ_NAR
% 0.08/0.31
% 0.08/0.31 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.08/0.31 % project in the Department of Mathematical Sciences at Carnegie
% 0.08/0.31 % Mellon University. Distributed under the Creative Commons copyleft
% 0.08/0.31 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.08/0.31 %------------------------------------------------------------------------------
% 0.08/0.31 thf(b_type,type,
% 0.08/0.31 b: $tType ).
% 0.08/0.31
% 0.08/0.31 thf(cL51,conjecture,
% 0.08/0.31 ! [Xx: b > $o] :
% 0.08/0.31 ? [Xy: b] :
% 0.08/0.31 ( ? [Xx0: b] : ( Xx @ Xx0 )
% 0.08/0.31 => ( Xx @ Xy ) ) ).
% 0.08/0.31
% 0.08/0.31 %------------------------------------------------------------------------------
% 0.08/0.31 ------------------------
% 0.84/0.89 ---- Embedded in THF ---
% 0.84/0.89 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.84/0.89 %%% Generated on Tue Feb 24 09:27:11 EST 2026
% 0.84/0.89 %%% using '$$dhol' embedding, version 1.3.0.
% 0.84/0.89 %%% Logic specification used:
% 0.84/0.89 %%% thf(spec, logic, $$dhol).
% 0.84/0.89
% 0.84/0.89 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.kDXdtsRDl1/DTF2DTF7657.p
% See solution above
% 0.84/0.89 ------------------------
% 1.03/0.90 ---- Cleaned THF ---
% 1.03/0.90 thf(b_type,type,
% 1.03/0.90 b: $tType ).
% 1.03/0.90
% 1.03/0.90 thf(cL51,conjecture,
% 1.03/0.90 ! [Xx: b > $o] :
% 1.03/0.90 ? [Xy: b] :
% 1.03/0.90 ( ? [Xx0: b] : ( Xx @ Xx0 )
% 1.03/0.90 => ( Xx @ Xy ) ) ).
% 1.03/0.90 ------------------------
% 1.03/0.91 % (7808)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_7657 for (3000ds/4Mi)
% 1.03/0.91 % (7807)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7657 for (3000ds/183Mi)
% 1.03/0.91 % (7810)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7657 for (3000ds/2Mi)
% 1.03/0.91 % (7809)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_7657 for (3000ds/27Mi)
% 1.03/0.91 % (7811)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_7657 for (3000ds/2Mi)
% 1.03/0.91 % (7812)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_7657 for (3000ds/275Mi)
% 1.03/0.91 % (7813)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7657 for (3000ds/18Mi)
% 1.03/0.91 % (7808)First to succeed.
% 1.03/0.91 % (7807)Also succeeded, but the first one will report.
% 1.03/0.91 % (7810)Also succeeded, but the first one will report.
% 1.03/0.91 % (7808)Refutation found. Thanks to Tanya!
% 1.03/0.91 % SZS status Theorem for DTF2THF_7657
% 1.03/0.91 % SZS output start Proof for DTF2THF_7657
% 1.03/0.91 thf(type_def_5, type, b: $tType).
% 1.03/0.91 thf(func_def_0, type, b: $tType).
% 1.03/0.91 thf(func_def_4, type, sK0: b > $o).
% 1.03/0.91 thf(func_def_5, type, sK1: b).
% 1.03/0.91 thf(f12,plain,(
% 1.03/0.91 $false),
% 1.03/0.91 inference(subsumption_resolution,[status(thm)],[f10,f11])).
% 1.03/0.91 thf(f11,plain,(
% 1.03/0.91 ( ! [X1 : b] : (($true != (sK0 @ X1))) )),
% 1.03/0.91 inference(cnf_transformation,[status(thm)],[f9])).
% 1.03/0.91 thf(f9,plain,(
% 1.03/0.91 ! [X1 : b] : (($true != (sK0 @ X1)) & ($true = (sK0 @ sK1)))),
% 1.03/0.91 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f6,f8,f7])).
% 1.03/0.91 thf(f7,plain,(
% 1.03/0.91 ? [X0 : b > $o] : ! [X1 : b] : (((X0 @ X1) != $true) & ? [X2 : b] : ((X0 @ X2) = $true)) => ! [X1 : b] : (($true != (sK0 @ X1)) & ? [X2 : b] : ($true = (sK0 @ X2)))),
% 1.03/0.91 introduced(definition,[],[choice_axiom])).
% 1.03/0.91 thf(f8,plain,(
% 1.03/0.91 ? [X2 : b] : ($true = (sK0 @ X2)) => ($true = (sK0 @ sK1))),
% 1.03/0.91 introduced(definition,[],[choice_axiom])).
% 1.03/0.91 thf(f6,plain,(
% 1.03/0.91 ? [X0 : b > $o] : ! [X1 : b] : (((X0 @ X1) != $true) & ? [X2 : b] : ((X0 @ X2) = $true))),
% 1.03/0.91 inference(ennf_transformation,[status(thm)],[f5])).
% 1.03/0.91 thf(f5,plain,(
% 1.03/0.91 ~! [X0 : b > $o] : ? [X1 : b] : (? [X2 : b] : ((X0 @ X2) = $true) => ((X0 @ X1) = $true))),
% 1.03/0.91 inference(fool_elimination,[status(thm)],[f4])).
% 1.03/0.91 thf(f4,plain,(
% 1.03/0.91 ~! [X0 : b > $o] : ? [X1 : b] : (? [X2 : b] : (X0 @ X2) => (X0 @ X1))),
% 1.03/0.91 inference(rectify,[status(thm)],[f2])).
% 1.03/0.91 thf(f2,negated_conjecture,(
% 1.03/0.91 ~! [X0 : b > $o] : ? [X1 : b] : (? [X2 : b] : (X0 @ X2) => (X0 @ X1))),
% 1.03/0.91 inference(negated_conjecture,[status(cth)],[f1])).
% 1.03/0.91 thf(f1,conjecture,(
% 1.03/0.91 ! [X0 : b > $o] : ? [X1 : b] : (? [X2 : b] : (X0 @ X2) => (X0 @ X1))),
% 1.03/0.91 file('/export/starexec/sandbox2/tmp/tmp.kDXdtsRDl1/DTF2THF_7657.p',cL51)).
% 1.03/0.91 thf(f10,plain,(
% 1.03/0.91 ($true = (sK0 @ sK1))),
% 1.03/0.91 inference(cnf_transformation,[status(thm)],[f9])).
% 1.03/0.91 % SZS output end Proof for DTF2THF_7657
% 1.03/0.91 % (7808)------------------------------
% 1.03/0.91 % (7808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.03/0.91 % (7808)Termination reason: Refutation
% 1.03/0.91
% 1.03/0.91 % (7808)Memory used [KB]: 5373
% 1.03/0.91 % (7808)Time elapsed: 0.002 s
% 1.03/0.91 % (7808)Instructions burned: 1 (million)
% 1.03/0.91 % (7808)------------------------------
% 1.03/0.91 % (7808)------------------------------
% 1.03/0.91 % (7806)Success in time 0.011 s
%------------------------------------------------------------------------------