%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO526^1 : TPTP v9.2.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n023.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 09:54:27 AM UTC 2026
% Result : Theorem 1.48s 1.28s
% Output : Refutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 50 ( 15 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 7 ( 5 ~; 0 |; 0 &; 0 @)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 12 ( 12 ^; 0 !; 0 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_2,type,
f: $i > $o ).
thf(func_def_3,type,
g: $i > $o ).
thf(f19,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ^ [Y0: $i] : b )
!= ( ^ [Y0: $i] : b ) ),
inference(definition_unfolding,[status(thm)],[f15,f17]) ).
thf(f17,plain,
( g
= ( ^ [Y0: $i] : b ) ),
inference(definition_unfolding,[status(thm)],[f12,f16]) ).
thf(f16,plain,
( f
= ( ^ [Y0: $i] : b ) ),
inference(definition_unfolding,[status(thm)],[f14,f13]) ).
thf(f13,plain,
a = b,
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
a = b,
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
( b
<=> a ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( b
<=> a ),
file('/export/starexec/sandbox/tmp/tmp.y2pA8EG2oB/DTF2THF_32251.p',ab) ).
thf(f14,plain,
( f
= ( ^ [Y0: $i] : a ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( f
= ( ^ [Y0: $i] : a ) ),
inference(fool_elimination,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X0: $i] : a )
= f ),
file('/export/starexec/sandbox/tmp/tmp.y2pA8EG2oB/DTF2THF_32251.p',fa) ).
thf(f12,plain,
f = g,
inference(cnf_transformation,[status(thm)],[f2]) ).
thf(f2,axiom,
f = g,
file('/export/starexec/sandbox/tmp/tmp.y2pA8EG2oB/DTF2THF_32251.p',fg) ).
thf(f15,plain,
( g
!= ( ^ [Y0: $i] : b ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( g
!= ( ^ [Y0: $i] : b ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( g
!= ( ^ [Y0: $i] : b ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
( ( ^ [X0: $i] : b )
!= g ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
( ( ^ [X0: $i] : b )
= g ),
file('/export/starexec/sandbox/tmp/tmp.y2pA8EG2oB/DTF2THF_32251.p',gb) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO526^1 : TPTP v9.2.1. Released v5.2.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n023.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 14:33:49 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
% 0.32/0.46 ---- Original DTF file ---
% 0.32/0.46 thf(spec,logic,$$dhol).
% 0.32/0.46 %------------------------------------------------------------------------------
% 0.32/0.46 % File : SYO526^1 : TPTP v9.2.1. Released v5.2.0.
% 0.32/0.46 % Domain : Syntactic
% 0.32/0.46 % Problem : The BQFQFE problem
% 0.32/0.46 % Version : Especial.
% 0.32/0.46 % English :
% 0.32/0.46
% 0.32/0.46 % Refs : [Bro11] Brown E. (2011), Email to Geoff Sutcliffe
% 0.32/0.46 % Source : [Bro11]
% 0.32/0.46 % Names : BQFQFE [Bro11]
% 0.32/0.46
% 0.32/0.46 % Status : Theorem
% 0.32/0.46 % Rating : 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 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 v5.2.0
% 0.32/0.46 % Syntax : Number of formulae : 8 ( 3 unt; 4 typ; 0 def)
% 0.32/0.46 % Number of atoms : 11 ( 3 equ; 0 cnn)
% 0.32/0.46 % Maximal formula atoms : 2 ( 2 avg)
% 0.32/0.46 % Number of connectives : 1 ( 0 ~; 0 |; 0 &; 0 @)
% 0.32/0.46 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.32/0.46 % Maximal formula depth : 2 ( 1 avg)
% 0.32/0.46 % Number of types : 2 ( 0 usr)
% 0.32/0.46 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.32/0.46 % Number of symbols : 5 ( 4 usr; 2 con; 0-2 aty)
% 0.32/0.46 % Number of variables : 2 ( 2 ^; 0 !; 0 ?; 2 :)
% 0.32/0.46 % SPC : TH0_THM_EQU_NAR
% 0.32/0.46
% 0.32/0.46 % Comments :
% 0.32/0.46 %------------------------------------------------------------------------------
% 0.32/0.46 thf(a,type,
% 0.32/0.46 a: $o ).
% 0.32/0.46
% 0.32/0.46 thf(b,type,
% 0.32/0.46 b: $o ).
% 0.32/0.46
% 0.32/0.46 thf(ab,axiom,
% 0.32/0.46 ( a
% 0.32/0.46 <=> b ) ).
% 0.32/0.46
% 0.32/0.46 thf(f,type,
% 0.32/0.46 f: $i > $o ).
% 0.32/0.46
% 0.32/0.46 thf(g,type,
% 0.32/0.46 g: $i > $o ).
% 0.32/0.46
% 0.32/0.46 thf(fg,axiom,
% 0.32/0.46 f = g ).
% 0.32/0.46
% 0.32/0.46 thf(fa,axiom,
% 0.32/0.46 ( f
% 0.32/0.46 = ( ^ [X: $i] : a ) ) ).
% 0.32/0.46
% 0.32/0.46 thf(gb,conjecture,
% 0.32/0.46 ( g
% 0.32/0.46 = ( ^ [X: $i] : b ) ) ).
% 0.32/0.46
% 0.32/0.46 %------------------------------------------------------------------------------
% 0.32/0.46 ------------------------
% 1.48/1.25 ---- Embedded in THF ---
% 1.48/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.25 %%% Generated on Tue Feb 24 14:33:50 EST 2026
% 1.48/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.25 %%% Logic specification used:
% 1.48/1.25 %%% thf(spec, logic, $$dhol).
% 1.48/1.25
% 1.48/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.y2pA8EG2oB/DTF2DTF32251.p
% See solution above
% 1.48/1.25 ------------------------
% 1.48/1.26 ---- Cleaned THF ---
% 1.48/1.26 thf(a,type,
% 1.48/1.26 a: $o ).
% 1.48/1.26
% 1.48/1.26 thf(b,type,
% 1.48/1.26 b: $o ).
% 1.48/1.26
% 1.48/1.26 thf(ab,axiom,
% 1.48/1.26 ( a
% 1.48/1.26 <=> b ) ).
% 1.48/1.26
% 1.48/1.26 thf(f,type,
% 1.48/1.26 f: $i > $o ).
% 1.48/1.26
% 1.48/1.26 thf(g,type,
% 1.48/1.26 g: $i > $o ).
% 1.48/1.26
% 1.48/1.26 thf(fg,axiom,
% 1.48/1.26 f = g ).
% 1.48/1.26
% 1.48/1.26 thf(fa,axiom,
% 1.48/1.26 ( f
% 1.48/1.26 = ( ^ [X: $i] : a ) ) ).
% 1.48/1.26
% 1.48/1.26 thf(gb,conjecture,
% 1.48/1.26 ( g
% 1.48/1.26 = ( ^ [X: $i] : b ) ) ).
% 1.48/1.26 ------------------------
% 1.48/1.28 % (32585)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_32251 for (2999ds/275Mi)
% 1.48/1.28 % (32585)First to succeed.
% 1.48/1.28 % (32585)Refutation found. Thanks to Tanya!
% 1.48/1.28 % SZS status Theorem for DTF2THF_32251
% 1.48/1.28 % SZS output start Proof for DTF2THF_32251
% 1.48/1.28 thf(func_def_2, type, f: $i > $o).
% 1.48/1.28 thf(func_def_3, type, g: $i > $o).
% 1.48/1.28 thf(f19,plain,(
% 1.48/1.28 $false),
% 1.48/1.28 inference(trivial_inequality_removal,[status(thm)],[f18])).
% 1.48/1.28 thf(f18,plain,(
% 1.48/1.28 ((^[Y0 : $i]: (b)) != (^[Y0 : $i]: (b)))),
% 1.48/1.28 inference(definition_unfolding,[status(thm)],[f15,f17])).
% 1.48/1.28 thf(f17,plain,(
% 1.48/1.28 (g = (^[Y0 : $i]: (b)))),
% 1.48/1.28 inference(definition_unfolding,[status(thm)],[f12,f16])).
% 1.48/1.28 thf(f16,plain,(
% 1.48/1.28 (f = (^[Y0 : $i]: (b)))),
% 1.48/1.28 inference(definition_unfolding,[status(thm)],[f14,f13])).
% 1.48/1.28 thf(f13,plain,(
% 1.48/1.28 (a = b)),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f9])).
% 1.48/1.28 thf(f9,plain,(
% 1.48/1.28 (a = b)),
% 1.48/1.28 inference(fool_elimination,[status(thm)],[f8])).
% 1.48/1.28 thf(f8,plain,(
% 1.48/1.28 b <=> a),
% 1.48/1.28 inference(rectify,[status(thm)],[f1])).
% 1.48/1.28 thf(f1,axiom,(
% 1.48/1.28 b <=> a),
% 1.48/1.28 file('/export/starexec/sandbox/tmp/tmp.y2pA8EG2oB/DTF2THF_32251.p',ab)).
% 1.48/1.28 thf(f14,plain,(
% 1.48/1.28 (f = (^[Y0 : $i]: (a)))),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f7])).
% 1.48/1.28 thf(f7,plain,(
% 1.48/1.28 (f = (^[Y0 : $i]: (a)))),
% 1.48/1.28 inference(fool_elimination,[status(thm)],[f3])).
% 1.48/1.28 thf(f3,axiom,(
% 1.48/1.28 ((^[X0 : $i] : (a)) = f)),
% 1.48/1.28 file('/export/starexec/sandbox/tmp/tmp.y2pA8EG2oB/DTF2THF_32251.p',fa)).
% 1.48/1.28 thf(f12,plain,(
% 1.48/1.28 (f = g)),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f2])).
% 1.48/1.28 thf(f2,axiom,(
% 1.48/1.28 (f = g)),
% 1.48/1.28 file('/export/starexec/sandbox/tmp/tmp.y2pA8EG2oB/DTF2THF_32251.p',fg)).
% 1.48/1.28 thf(f15,plain,(
% 1.48/1.28 (g != (^[Y0 : $i]: (b)))),
% 1.48/1.28 inference(cnf_transformation,[status(thm)],[f11])).
% 1.48/1.28 thf(f11,plain,(
% 1.48/1.28 (g != (^[Y0 : $i]: (b)))),
% 1.48/1.28 inference(flattening,[status(thm)],[f10])).
% 1.48/1.28 thf(f10,plain,(
% 1.48/1.28 ~(g = (^[Y0 : $i]: (b)))),
% 1.48/1.28 inference(fool_elimination,[status(thm)],[f5])).
% 1.48/1.28 thf(f5,negated_conjecture,(
% 1.48/1.28 ~((^[X0 : $i] : (b)) = g)),
% 1.48/1.28 inference(negated_conjecture,[status(cth)],[f4])).
% 1.48/1.28 thf(f4,conjecture,(
% 1.48/1.28 ((^[X0 : $i] : (b)) = g)),
% 1.48/1.28 file('/export/starexec/sandbox/tmp/tmp.y2pA8EG2oB/DTF2THF_32251.p',gb)).
% 1.48/1.28 % SZS output end Proof for DTF2THF_32251
% 1.48/1.28 % (32585)------------------------------
% 1.48/1.28 % (32585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (32585)Termination reason: Refutation
% 1.48/1.28
% 1.48/1.28 % (32585)Memory used [KB]: 5373
% 1.48/1.28 % (32585)Time elapsed: 0.002 s
% 1.48/1.28 % (32585)Instructions burned: 1 (million)
% 1.48/1.28 % (32585)------------------------------
% 1.48/1.28 % (32585)------------------------------
% 1.48/1.28 % (32579)Success in time 0.012 s
%------------------------------------------------------------------------------