%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO286^5 : 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 : n010.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 1.12s 1.10s
% Output : Refutation 1.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 78 ( 19 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 53 ( 8 ~; 0 |; 8 &; 28 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 17 ( 0 ^; 9 !; 8 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cQ: $i > $o ).
thf(func_def_2,type,
cR: $i > $o ).
thf(f14,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f12,f11]) ).
thf(f11,plain,
! [X1: $i > $o] :
( $true
= ( X1 @ y ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( cR @ sK0 )
= $true )
& ( ( cQ @ y )
!= $true )
& ! [X1: $i > $o] :
( $true
= ( X1 @ y ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9]) ).
thf(f9,plain,
( ? [X0: $i] :
( ( cR @ X0 )
= $true )
=> ( ( cR @ sK0 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ? [X0: $i] :
( ( cR @ X0 )
= $true )
& ( ( cQ @ y )
!= $true )
& ! [X1: $i > $o] :
( $true
= ( X1 @ y ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ? [X1: $i] :
( ( cR @ X1 )
= $true )
& ( ( cQ @ y )
!= $true )
& ! [X0: $i > $o] :
( ( X0 @ y )
= $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ( cQ @ y )
!= $true )
& ? [X1: $i] :
( ( cR @ X1 )
= $true )
& ! [X0: $i > $o] :
( ( X0 @ y )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: $i > $o] :
( ( X0 @ y )
= $true )
=> ( ? [X1: $i] :
( ( cR @ X1 )
= $true )
=> ( ( cQ @ y )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: $i > $o] : ( X0 @ y )
=> ( ? [X1: $i] : ( cR @ X1 )
=> ( cQ @ y ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i > $o] : ( X0 @ y )
=> ( ? [X1: $i] : ( cR @ X1 )
=> ( cQ @ y ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: $i > $o] : ( X0 @ y )
=> ( ? [X1: $i] : ( cR @ X1 )
=> ( cQ @ y ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XghEtPQBwK/DTF2THF_27863.p',cTEST1) ).
thf(f12,plain,
( ( cQ @ y )
!= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SYO286^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.32 % Computer : n010.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue Feb 24 14:27:18 EST 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.41 ---- Original DTF file ---
% 0.16/0.41 thf(spec,logic,$$dhol).
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 % File : SYO286^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.41 % Domain : Syntactic
% 0.16/0.41 % Problem : TPS problem from BASIC-HO-THMS
% 0.16/0.41 % Version : Especial.
% 0.16/0.41 % English :
% 0.16/0.41
% 0.16/0.41 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.41 % Source : [Bro09]
% 0.16/0.41 % Names : tps_0675 [Bro09]
% 0.16/0.41
% 0.16/0.41 % Status : Theorem
% 0.16/0.41 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.33 v6.1.0, 0.00 v4.0.0
% 0.16/0.41 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.16/0.41 % Number of atoms : 2 ( 0 equ; 0 cnn)
% 0.16/0.41 % Maximal formula atoms : 2 ( 2 avg)
% 0.16/0.41 % Number of connectives : 5 ( 0 ~; 0 |; 0 &; 3 @)
% 0.16/0.41 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.16/0.41 % Maximal formula depth : 5 ( 5 avg)
% 0.16/0.41 % Number of types : 2 ( 0 usr)
% 0.16/0.41 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.16/0.41 % Number of symbols : 3 ( 3 usr; 1 con; 0-1 aty)
% 0.16/0.41 % Number of variables : 2 ( 0 ^; 1 !; 1 ?; 2 :)
% 0.16/0.41 % SPC : TH0_THM_NEQ_NAR
% 0.16/0.41
% 0.16/0.41 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.41 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.41 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.41 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 thf(y,type,
% 0.16/0.41 y: $i ).
% 0.16/0.41
% 0.16/0.41 thf(cQ,type,
% 0.16/0.41 cQ: $i > $o ).
% 0.16/0.41
% 0.16/0.41 thf(cR,type,
% 0.16/0.41 cR: $i > $o ).
% 0.16/0.41
% 0.16/0.41 thf(cTEST1,conjecture,
% 0.16/0.41 ( ! [Xp: $i > $o] : ( Xp @ y )
% 0.16/0.41 => ( ? [Xx: $i] : ( cR @ Xx )
% 0.16/0.41 => ( cQ @ y ) ) ) ).
% 0.16/0.41
% 0.16/0.41 %------------------------------------------------------------------------------
% 0.16/0.41 ------------------------
% 1.12/1.08 ---- Embedded in THF ---
% 1.12/1.08 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.12/1.08 %%% Generated on Tue Feb 24 14:27:18 EST 2026
% 1.12/1.08 %%% using '$$dhol' embedding, version 1.3.0.
% 1.12/1.08 %%% Logic specification used:
% 1.12/1.08 %%% thf(spec, logic, $$dhol).
% 1.12/1.08
% 1.12/1.08 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.XghEtPQBwK/DTF2DTF27863.p
% See solution above
% 1.12/1.08 ------------------------
% 1.12/1.08 ---- Cleaned THF ---
% 1.12/1.08 thf(y,type,
% 1.12/1.08 y: $i ).
% 1.12/1.08
% 1.12/1.08 thf(cQ,type,
% 1.12/1.08 cQ: $i > $o ).
% 1.12/1.08
% 1.12/1.08 thf(cR,type,
% 1.12/1.08 cR: $i > $o ).
% 1.12/1.08
% 1.12/1.08 thf(cTEST1,conjecture,
% 1.12/1.08 ( ! [Xp: $i > $o] : ( Xp @ y )
% 1.12/1.08 => ( ? [Xx: $i] : ( cR @ Xx )
% 1.12/1.08 => ( cQ @ y ) ) ) ).
% 1.12/1.08 ------------------------
% 1.12/1.10 % (27984)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_27863 for (3000ds/4Mi)
% 1.12/1.10 % (27987)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_27863 for (3000ds/2Mi)
% 1.12/1.10 % (27988)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_27863 for (3000ds/275Mi)
% 1.12/1.10 % (27989)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27863 for (3000ds/18Mi)
% 1.12/1.10 % (27982)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27863 for (3000ds/183Mi)
% 1.12/1.10 % (27986)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27863 for (3000ds/2Mi)
% 1.12/1.10 % (27985)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_27863 for (3000ds/27Mi)
% 1.12/1.10 % (27982)First to succeed.
% 1.12/1.10 % (27989)Also succeeded, but the first one will report.
% 1.12/1.10 % (27984)Also succeeded, but the first one will report.
% 1.12/1.10 % (27982)Refutation found. Thanks to Tanya!
% 1.12/1.10 % SZS status Theorem for DTF2THF_27863
% 1.12/1.10 % SZS output start Proof for DTF2THF_27863
% 1.12/1.10 thf(func_def_1, type, cQ: $i > $o).
% 1.12/1.10 thf(func_def_2, type, cR: $i > $o).
% 1.12/1.10 thf(f14,plain,(
% 1.12/1.10 $false),
% 1.12/1.10 inference(subsumption_resolution,[status(thm)],[f12,f11])).
% 1.12/1.10 thf(f11,plain,(
% 1.12/1.10 ( ! [X1 : $i > $o] : (($true = (X1 @ y))) )),
% 1.12/1.10 inference(cnf_transformation,[status(thm)],[f10])).
% 1.12/1.10 thf(f10,plain,(
% 1.12/1.10 ((cR @ sK0) = $true) & ((cQ @ y) != $true) & ! [X1 : $i > $o] : ($true = (X1 @ y))),
% 1.12/1.10 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f8,f9])).
% 1.12/1.10 thf(f9,plain,(
% 1.12/1.10 ? [X0 : $i] : ((cR @ X0) = $true) => ((cR @ sK0) = $true)),
% 1.12/1.10 introduced(definition,[],[choice_axiom])).
% 1.12/1.10 thf(f8,plain,(
% 1.12/1.10 ? [X0 : $i] : ((cR @ X0) = $true) & ((cQ @ y) != $true) & ! [X1 : $i > $o] : ($true = (X1 @ y))),
% 1.12/1.10 inference(rectify,[status(thm)],[f7])).
% 1.12/1.10 thf(f7,plain,(
% 1.12/1.10 ? [X1 : $i] : ((cR @ X1) = $true) & ((cQ @ y) != $true) & ! [X0 : $i > $o] : ((X0 @ y) = $true)),
% 1.12/1.10 inference(flattening,[status(thm)],[f6])).
% 1.12/1.10 thf(f6,plain,(
% 1.12/1.10 (((cQ @ y) != $true) & ? [X1 : $i] : ((cR @ X1) = $true)) & ! [X0 : $i > $o] : ((X0 @ y) = $true)),
% 1.12/1.10 inference(ennf_transformation,[status(thm)],[f5])).
% 1.12/1.10 thf(f5,plain,(
% 1.12/1.10 ~(! [X0 : $i > $o] : ((X0 @ y) = $true) => (? [X1 : $i] : ((cR @ X1) = $true) => ((cQ @ y) = $true)))),
% 1.12/1.10 inference(fool_elimination,[status(thm)],[f4])).
% 1.12/1.10 thf(f4,plain,(
% 1.12/1.10 ~(! [X0 : $i > $o] : (X0 @ y) => (? [X1 : $i] : (cR @ X1) => (cQ @ y)))),
% 1.12/1.10 inference(rectify,[status(thm)],[f2])).
% 1.12/1.10 thf(f2,negated_conjecture,(
% 1.12/1.10 ~(! [X0 : $i > $o] : (X0 @ y) => (? [X1 : $i] : (cR @ X1) => (cQ @ y)))),
% 1.12/1.10 inference(negated_conjecture,[status(cth)],[f1])).
% 1.12/1.10 thf(f1,conjecture,(
% 1.12/1.10 ! [X0 : $i > $o] : (X0 @ y) => (? [X1 : $i] : (cR @ X1) => (cQ @ y))),
% 1.12/1.10 file('/export/starexec/sandbox2/tmp/tmp.XghEtPQBwK/DTF2THF_27863.p',cTEST1)).
% 1.12/1.10 thf(f12,plain,(
% 1.12/1.10 ((cQ @ y) != $true)),
% 1.12/1.10 inference(cnf_transformation,[status(thm)],[f10])).
% 1.12/1.10 % SZS output end Proof for DTF2THF_27863
% 1.12/1.10 % (27982)------------------------------
% 1.12/1.10 % (27982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.12/1.10 % (27982)Termination reason: Refutation
% 1.12/1.10
% 1.12/1.10 % (27982)Memory used [KB]: 5373
% 1.12/1.10 % (27982)Time elapsed: 0.002 s
% 1.12/1.10 % (27982)Instructions burned: 1 (million)
% 1.12/1.10 % (27982)------------------------------
% 1.12/1.10 % (27982)------------------------------
% 1.12/1.10 % (27980)Success in time 0.011 s
%------------------------------------------------------------------------------