%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV168^5 : 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 : n026.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 09:40:27 AM UTC 2026
% Result : Theorem 1.63s 1.47s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 22 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 79 ( 7 ~; 0 |; 8 &; 60 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 30 ( 30 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 75 ( 75 ^; 0 !; 0 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
q: ( a > a > a ) > a ).
thf(func_def_2,type,
p: ( a > a > a ) > a ).
thf(f12,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f11,f10]) ).
thf(f10,plain,
( q
= ( ^ [Y0: a > a > a] :
( Y0
@ ( q
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( q
@ ^ [Y1: a,Y2: a] : Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ( q
= ( ^ [Y0: a > a > a] :
( Y0
@ ( q
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( q
@ ^ [Y1: a,Y2: a] : Y2 ) ) ) )
& ( p
= ( ^ [Y0: a > a > a] :
( Y0
@ ( q
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( q
@ ^ [Y1: a,Y2: a] : Y2 ) ) ) )
& ( q != p ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ( q != p )
& ( p
= ( ^ [Y0: a > a > a] :
( Y0
@ ( q
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( q
@ ^ [Y1: a,Y2: a] : Y2 ) ) ) )
& ( q
= ( ^ [Y0: a > a > a] :
( Y0
@ ( q
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( q
@ ^ [Y1: a,Y2: a] : Y2 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( p
= ( ^ [Y0: a > a > a] :
( Y0
@ ( q
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( q
@ ^ [Y1: a,Y2: a] : Y2 ) ) ) )
& ( q
= ( ^ [Y0: a > a > a] :
( Y0
@ ( q
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( q
@ ^ [Y1: a,Y2: a] : Y2 ) ) ) ) )
=> ( q = p ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( p
= ( ^ [X0: a > a > a] :
( X0
@ ( q
@ ^ [X1: a,X2: a] : X1 )
@ ( q
@ ^ [X3: a,X4: a] : X4 ) ) ) )
& ( ( ^ [X5: a > a > a] :
( X5
@ ( q
@ ^ [X6: a,X7: a] : X6 )
@ ( q
@ ^ [X8: a,X9: a] : X9 ) ) )
= q ) )
=> ( q = p ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( p
= ( ^ [X0: a > a > a] :
( X0
@ ( q
@ ^ [X1: a,X2: a] : X1 )
@ ( q
@ ^ [X1: a,X2: a] : X2 ) ) ) )
& ( ( ^ [X0: a > a > a] :
( X0
@ ( q
@ ^ [X1: a,X2: a] : X1 )
@ ( q
@ ^ [X1: a,X2: a] : X2 ) ) )
= q ) )
=> ( q = p ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ( p
= ( ^ [X0: a > a > a] :
( X0
@ ( q
@ ^ [X1: a,X2: a] : X1 )
@ ( q
@ ^ [X1: a,X2: a] : X2 ) ) ) )
& ( ( ^ [X0: a > a > a] :
( X0
@ ( q
@ ^ [X1: a,X2: a] : X1 )
@ ( q
@ ^ [X1: a,X2: a] : X2 ) ) )
= q ) )
=> ( q = p ) ),
file('/export/starexec/sandbox/tmp/tmp.KF9FuFBN5N/DTF2THF_22167.p',cTHM188_PARTIAL_pme) ).
thf(f11,plain,
( q
!= ( ^ [Y0: a > a > a] :
( Y0
@ ( q
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( q
@ ^ [Y1: a,Y2: a] : Y2 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f8,f9]) ).
thf(f9,plain,
( p
= ( ^ [Y0: a > a > a] :
( Y0
@ ( q
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( q
@ ^ [Y1: a,Y2: a] : Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f8,plain,
q != p,
inference(cnf_transformation,[status(thm)],[f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV168^5 : 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
% 0.15/0.34 % Computer : n026.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:41:40 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.47 ---- Original DTF file ---
% 0.21/0.48 thf(spec,logic,$$dhol).
% 0.21/0.48 %------------------------------------------------------------------------------
% 0.21/0.48 % File : SEV168^5 : TPTP v9.2.1. Released v4.0.0.
% 0.21/0.48 % Domain : Set Theory
% 0.21/0.48 % Problem : TPS problem from PAIRS-THMS
% 0.21/0.48 % Version : Especial.
% 0.21/0.48 % English :
% 0.21/0.48
% 0.21/0.48 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.21/0.48 % Source : [Bro09]
% 0.21/0.48 % Names : tps_0889 [Bro09]
% 0.21/0.48
% 0.21/0.48 % Status : Theorem
% 0.21/0.48 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.18 v7.5.0, 0.00 v6.2.0, 0.29 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.21/0.48 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.21/0.48 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.21/0.48 % Maximal formula atoms : 3 ( 3 avg)
% 0.21/0.48 % Number of connectives : 10 ( 0 ~; 0 |; 1 &; 8 @)
% 0.21/0.48 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.21/0.48 % Maximal formula depth : 3 ( 3 avg)
% 0.21/0.48 % Number of types : 1 ( 1 usr)
% 0.21/0.48 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.21/0.48 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.21/0.48 % Number of variables : 10 ( 10 ^; 0 !; 0 ?; 10 :)
% 0.21/0.48 % SPC : TH0_THM_EQU_NAR
% 0.21/0.48
% 0.21/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.21/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.21/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.21/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.21/0.48 %------------------------------------------------------------------------------
% 0.21/0.48 thf(a_type,type,
% 0.21/0.48 a: $tType ).
% 0.21/0.48
% 0.21/0.48 thf(q,type,
% 0.21/0.48 q: ( a > a > a ) > a ).
% 0.21/0.48
% 0.21/0.48 thf(p,type,
% 0.21/0.48 p: ( a > a > a ) > a ).
% 0.21/0.48
% 0.21/0.48 thf(cTHM188_PARTIAL_pme,conjecture,
% 0.21/0.48 ( ( ( q
% 0.21/0.48 = ( ^ [Xg: a > a > a] :
% 0.21/0.48 ( Xg
% 0.21/0.48 @ ( q
% 0.21/0.48 @ ^ [Xx: a,Xy: a] : Xx )
% 0.21/0.48 @ ( q
% 0.21/0.48 @ ^ [Xx: a,Xy: a] : Xy ) ) ) )
% 0.21/0.48 & ( p
% 0.21/0.48 = ( ^ [Xg: a > a > a] :
% 0.21/0.48 ( Xg
% 0.21/0.48 @ ( q
% 0.21/0.48 @ ^ [Xx: a,Xy: a] : Xx )
% 0.21/0.48 @ ( q
% 0.21/0.48 @ ^ [Xx: a,Xy: a] : Xy ) ) ) ) )
% 0.21/0.48 => ( p = q ) ) ).
% 0.21/0.48
% 0.21/0.48 %------------------------------------------------------------------------------
% 0.21/0.48 ------------------------
% 1.63/1.45 ---- Embedded in THF ---
% 1.63/1.45 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.63/1.45 %%% Generated on Tue Feb 24 12:41:41 EST 2026
% 1.63/1.45 %%% using '$$dhol' embedding, version 1.3.0.
% 1.63/1.45 %%% Logic specification used:
% 1.63/1.45 %%% thf(spec, logic, $$dhol).
% 1.63/1.45
% 1.63/1.45 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.KF9FuFBN5N/DTF2DTF22167.p
% See solution above
% 1.63/1.45 ------------------------
% 1.63/1.45 ---- Cleaned THF ---
% 1.63/1.46 thf(a_type,type,
% 1.63/1.46 a: $tType ).
% 1.63/1.46
% 1.63/1.46 thf(q,type,
% 1.63/1.46 q: ( a > a > a ) > a ).
% 1.63/1.46
% 1.63/1.46 thf(p,type,
% 1.63/1.46 p: ( a > a > a ) > a ).
% 1.63/1.46
% 1.63/1.46 thf(cTHM188_PARTIAL_pme,conjecture,
% 1.63/1.46 ( ( ( q
% 1.63/1.46 = ( ^ [Xg: a > a > a] :
% 1.63/1.46 ( Xg
% 1.63/1.46 @ ( q
% 1.63/1.46 @ ^ [Xx: a,Xy: a] : Xx )
% 1.63/1.46 @ ( q
% 1.63/1.46 @ ^ [Xx: a,Xy: a] : Xy ) ) ) )
% 1.63/1.46 & ( p
% 1.63/1.46 = ( ^ [Xg: a > a > a] :
% 1.63/1.46 ( Xg
% 1.63/1.46 @ ( q
% 1.63/1.46 @ ^ [Xx: a,Xy: a] : Xx )
% 1.63/1.46 @ ( q
% 1.63/1.46 @ ^ [Xx: a,Xy: a] : Xy ) ) ) ) )
% 1.63/1.46 => ( p = q ) ) ).
% 1.63/1.46 ------------------------
% 1.63/1.47 % (22327)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22167 for (3000ds/183Mi)
% 1.63/1.47 % (22327)First to succeed.
% 1.63/1.47 % (22327)Refutation found. Thanks to Tanya!
% 1.63/1.47 % SZS status Theorem for DTF2THF_22167
% 1.63/1.47 % SZS output start Proof for DTF2THF_22167
% 1.63/1.47 thf(type_def_5, type, a: $tType).
% 1.63/1.47 thf(func_def_0, type, a: $tType).
% 1.63/1.47 thf(func_def_1, type, q: (a > a > a) > a).
% 1.63/1.47 thf(func_def_2, type, p: (a > a > a) > a).
% 1.63/1.47 thf(f12,plain,(
% 1.63/1.47 $false),
% 1.63/1.47 inference(subsumption_resolution,[status(thm)],[f11,f10])).
% 1.63/1.47 thf(f10,plain,(
% 1.63/1.47 (q = (^[Y0 : a > a > a]: (Y0 @ (q @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (q @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))))),
% 1.63/1.47 inference(cnf_transformation,[status(thm)],[f7])).
% 1.63/1.47 thf(f7,plain,(
% 1.63/1.47 (q = (^[Y0 : a > a > a]: (Y0 @ (q @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (q @ (^[Y1 : a]: ((^[Y2 : a]: (Y2)))))))) & (p = (^[Y0 : a > a > a]: (Y0 @ (q @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (q @ (^[Y1 : a]: ((^[Y2 : a]: (Y2)))))))) & (q != p)),
% 1.63/1.47 inference(flattening,[status(thm)],[f6])).
% 1.63/1.47 thf(f6,plain,(
% 1.63/1.47 (q != p) & ((p = (^[Y0 : a > a > a]: (Y0 @ (q @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (q @ (^[Y1 : a]: ((^[Y2 : a]: (Y2)))))))) & (q = (^[Y0 : a > a > a]: (Y0 @ (q @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (q @ (^[Y1 : a]: ((^[Y2 : a]: (Y2)))))))))),
% 1.63/1.47 inference(ennf_transformation,[status(thm)],[f5])).
% 1.63/1.47 thf(f5,plain,(
% 1.63/1.47 ~(((p = (^[Y0 : a > a > a]: (Y0 @ (q @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (q @ (^[Y1 : a]: ((^[Y2 : a]: (Y2)))))))) & (q = (^[Y0 : a > a > a]: (Y0 @ (q @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (q @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))))) => (q = p))),
% 1.63/1.47 inference(fool_elimination,[status(thm)],[f4])).
% 1.63/1.47 thf(f4,plain,(
% 1.63/1.47 ~(((p = (^[X0 : a > a > a] : (X0 @ (q @ (^[X1 : a, X2 : a] : (X1))) @ (q @ (^[X3 : a, X4 : a] : (X4)))))) & ((^[X5 : a > a > a] : (X5 @ (q @ (^[X6 : a, X7 : a] : (X6))) @ (q @ (^[X8 : a, X9 : a] : (X9))))) = q)) => (q = p))),
% 1.63/1.47 inference(rectify,[status(thm)],[f2])).
% 1.63/1.47 thf(f2,negated_conjecture,(
% 1.63/1.47 ~(((p = (^[X0 : a > a > a] : (X0 @ (q @ (^[X1 : a, X2 : a] : (X1))) @ (q @ (^[X1 : a, X2 : a] : (X2)))))) & ((^[X0 : a > a > a] : (X0 @ (q @ (^[X1 : a, X2 : a] : (X1))) @ (q @ (^[X1 : a, X2 : a] : (X2))))) = q)) => (q = p))),
% 1.63/1.47 inference(negated_conjecture,[status(cth)],[f1])).
% 1.63/1.47 thf(f1,conjecture,(
% 1.63/1.47 ((p = (^[X0 : a > a > a] : (X0 @ (q @ (^[X1 : a, X2 : a] : (X1))) @ (q @ (^[X1 : a, X2 : a] : (X2)))))) & ((^[X0 : a > a > a] : (X0 @ (q @ (^[X1 : a, X2 : a] : (X1))) @ (q @ (^[X1 : a, X2 : a] : (X2))))) = q)) => (q = p)),
% 1.63/1.47 file('/export/starexec/sandbox/tmp/tmp.KF9FuFBN5N/DTF2THF_22167.p',cTHM188_PARTIAL_pme)).
% 1.63/1.47 thf(f11,plain,(
% 1.63/1.47 (q != (^[Y0 : a > a > a]: (Y0 @ (q @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (q @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))))),
% 1.63/1.47 inference(definition_unfolding,[status(thm)],[f8,f9])).
% 1.63/1.47 thf(f9,plain,(
% 1.63/1.47 (p = (^[Y0 : a > a > a]: (Y0 @ (q @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (q @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))))),
% 1.63/1.47 inference(cnf_transformation,[status(thm)],[f7])).
% 1.63/1.47 thf(f8,plain,(
% 1.63/1.47 (q != p)),
% 1.63/1.47 inference(cnf_transformation,[status(thm)],[f7])).
% 1.63/1.47 % SZS output end Proof for DTF2THF_22167
% 1.63/1.47 % (22327)------------------------------
% 1.63/1.47 % (22327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.47 % (22327)Termination reason: Refutation
% 1.63/1.47
% 1.63/1.47 % (22327)Memory used [KB]: 5373
% 1.63/1.47 % (22327)Time elapsed: 0.002 s
% 1.63/1.47 % (22327)Instructions burned: 2 (million)
% 1.63/1.47 % (22327)------------------------------
% 1.63/1.47 % (22327)------------------------------
% 1.63/1.47 % (22326)Success in time 0.011 s
%------------------------------------------------------------------------------