%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV163^5 : 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 : n020.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 1.46s 1.29s
% Output : Refutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2
% Syntax : Number of formulae : 10 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 18 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 89 ( 8 ~; 0 |; 4 &; 72 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 54 ( 54 >; 0 *; 0 +; 0 <<)
% Number of symbols : 3 ( 1 usr; 1 con; 0-2 aty)
% Number of variables : 96 ( 90 ^; 4 !; 2 ?; 96 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_7,type,
sK0: ( a > a > a ) > a ).
thf(f11,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f9,f10]) ).
thf(f10,plain,
( ( ^ [Y0: a > a > a] :
( Y0
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
!= sK0 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ( ^ [Y0: a > a > a] :
( Y0
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
!= sK0 )
& ( ( ^ [Y0: a > a > a] :
( Y0
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= sK0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: ( a > a > a ) > a] :
( ( ( ^ [Y0: a > a > a] :
( Y0
@ ( X0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( X0
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
!= X0 )
& ( ( ^ [Y0: a > a > a] :
( Y0
@ ( X0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( X0
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= X0 ) )
=> ( ( ( ^ [Y0: a > a > a] :
( Y0
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
!= sK0 )
& ( ( ^ [Y0: a > a > a] :
( Y0
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: ( a > a > a ) > a] :
( ( ( ^ [Y0: a > a > a] :
( Y0
@ ( X0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( X0
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
!= X0 )
& ( ( ^ [Y0: a > a > a] :
( Y0
@ ( X0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( X0
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= X0 ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: ( a > a > a ) > a] :
( ( ( ^ [Y0: a > a > a] :
( Y0
@ ( X0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( X0
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= X0 )
=> ( ( ^ [Y0: a > a > a] :
( Y0
@ ( X0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( X0
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= X0 ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: ( a > a > a ) > a] :
( ( ( ^ [X1: a > a > a] :
( X1
@ ( X0
@ ^ [X2: a,X3: a] : X2 )
@ ( X0
@ ^ [X4: a,X5: a] : X5 ) ) )
= X0 )
=> ( X0
= ( ^ [X6: a > a > a] :
( X6
@ ( X0
@ ^ [X7: a,X8: a] : X7 )
@ ( X0
@ ^ [X9: a,X10: a] : X10 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: ( a > a > a ) > a] :
( ( ( ^ [X1: a > a > a] :
( X1
@ ( X0
@ ^ [X2: a,X3: a] : X2 )
@ ( X0
@ ^ [X2: a,X3: a] : X3 ) ) )
= X0 )
=> ( X0
= ( ^ [X1: a > a > a] :
( X1
@ ( X0
@ ^ [X2: a,X3: a] : X2 )
@ ( X0
@ ^ [X2: a,X3: a] : X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: ( a > a > a ) > a] :
( ( ( ^ [X1: a > a > a] :
( X1
@ ( X0
@ ^ [X2: a,X3: a] : X2 )
@ ( X0
@ ^ [X2: a,X3: a] : X3 ) ) )
= X0 )
=> ( X0
= ( ^ [X1: a > a > a] :
( X1
@ ( X0
@ ^ [X2: a,X3: a] : X2 )
@ ( X0
@ ^ [X2: a,X3: a] : X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.g4POOFKHLA/DTF2THF_11261.p',cTHM187_pme) ).
thf(f9,plain,
( ( ^ [Y0: a > a > a] :
( Y0
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y1 )
@ ( sK0
@ ^ [Y1: a,Y2: a] : Y2 ) ) )
= sK0 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV163^5 : 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 : n020.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 12:41:27 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
% 0.20/0.47 ---- Original DTF file ---
% 0.31/0.47 thf(spec,logic,$$dhol).
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % File : SEV163^5 : TPTP v9.2.1. Released v4.0.0.
% 0.31/0.47 % Domain : Set Theory
% 0.31/0.47 % Problem : TPS problem THM187
% 0.31/0.47 % Version : Especial.
% 0.31/0.47 % English : Basic theorem about pairing.
% 0.31/0.47
% 0.31/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.31/0.47 % Source : [Bro09]
% 0.31/0.47 % Names : tps_0155 [Bro09]
% 0.31/0.47 % : THM187 [TPS]
% 0.31/0.47
% 0.31/0.47 % Status : Theorem
% 0.31/0.47 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 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 v4.0.1, 0.33 v4.0.0
% 0.31/0.47 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.31/0.47 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.31/0.47 % Maximal formula atoms : 2 ( 2 avg)
% 0.31/0.47 % Number of connectives : 9 ( 0 ~; 0 |; 0 &; 8 @)
% 0.31/0.47 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.31/0.47 % Maximal formula depth : 3 ( 3 avg)
% 0.31/0.47 % Number of types : 1 ( 1 usr)
% 0.31/0.47 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.31/0.47 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.31/0.47 % Number of variables : 11 ( 10 ^; 1 !; 0 ?; 11 :)
% 0.31/0.47 % SPC : TH0_THM_EQU_NAR
% 0.31/0.47
% 0.31/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.31/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.31/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.31/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.31/0.47 % : Polymorphic definitions expanded.
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 thf(a_type,type,
% 0.31/0.47 a: $tType ).
% 0.31/0.47
% 0.31/0.47 thf(cTHM187_pme,conjecture,
% 0.31/0.47 ! [Xp: ( a > a > a ) > a] :
% 0.31/0.47 ( ( Xp
% 0.31/0.47 = ( ^ [Xg: a > a > a] :
% 0.31/0.47 ( Xg
% 0.31/0.47 @ ( Xp
% 0.31/0.47 @ ^ [Xx: a,Xy: a] : Xx )
% 0.31/0.47 @ ( Xp
% 0.31/0.47 @ ^ [Xx: a,Xy: a] : Xy ) ) ) )
% 0.31/0.47 => ( ( ^ [Xg: a > a > a] :
% 0.31/0.47 ( Xg
% 0.31/0.47 @ ( Xp
% 0.31/0.47 @ ^ [Xx: a,Xy: a] : Xx )
% 0.31/0.47 @ ( Xp
% 0.31/0.47 @ ^ [Xx: a,Xy: a] : Xy ) ) )
% 0.31/0.47 = Xp ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 1.46/1.26 ---- Embedded in THF ---
% 1.46/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.46/1.26 %%% Generated on Tue Feb 24 12:41:28 EST 2026
% 1.46/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.46/1.26 %%% Logic specification used:
% 1.46/1.26 %%% thf(spec, logic, $$dhol).
% 1.46/1.26
% 1.46/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.g4POOFKHLA/DTF2DTF11261.p
% See solution above
% 1.46/1.26 ------------------------
% 1.46/1.27 ---- Cleaned THF ---
% 1.46/1.27 thf(a_type,type,
% 1.46/1.27 a: $tType ).
% 1.46/1.27
% 1.46/1.27 thf(cTHM187_pme,conjecture,
% 1.46/1.27 ! [Xp: ( a > a > a ) > a] :
% 1.46/1.27 ( ( Xp
% 1.46/1.27 = ( ^ [Xg: a > a > a] :
% 1.46/1.27 ( Xg
% 1.46/1.27 @ ( Xp
% 1.46/1.27 @ ^ [Xx: a,Xy: a] : Xx )
% 1.46/1.27 @ ( Xp
% 1.46/1.27 @ ^ [Xx: a,Xy: a] : Xy ) ) ) )
% 1.46/1.27 => ( ( ^ [Xg: a > a > a] :
% 1.46/1.27 ( Xg
% 1.46/1.27 @ ( Xp
% 1.46/1.27 @ ^ [Xx: a,Xy: a] : Xx )
% 1.46/1.27 @ ( Xp
% 1.46/1.27 @ ^ [Xx: a,Xy: a] : Xy ) ) )
% 1.46/1.27 = Xp ) ) ).
% 1.46/1.27 ------------------------
% 1.46/1.28 % (11453)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_11261 for (3000ds/2Mi)
% 1.46/1.28 % (11454)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_11261 for (3000ds/275Mi)
% 1.46/1.29 % (11454)First to succeed.
% 1.46/1.29 % (11449)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11261 for (3000ds/183Mi)
% 1.46/1.29 % (11453)Instruction limit reached!
% 1.46/1.29 % (11453)------------------------------
% 1.46/1.29 % (11453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (11453)Termination reason: Unknown
% 1.46/1.29 % (11453)Termination phase: Saturation
% 1.46/1.29
% 1.46/1.29 % (11453)Memory used [KB]: 5500
% 1.46/1.29 % (11453)Time elapsed: 0.002 s
% 1.46/1.29 % (11453)Instructions burned: 2 (million)
% 1.46/1.29 % (11453)------------------------------
% 1.46/1.29 % (11453)------------------------------
% 1.46/1.29 % (11449)Also succeeded, but the first one will report.
% 1.46/1.29 % (11454)Refutation found. Thanks to Tanya!
% 1.46/1.29 % SZS status Theorem for DTF2THF_11261
% 1.46/1.29 % SZS output start Proof for DTF2THF_11261
% 1.46/1.29 thf(type_def_5, type, a: $tType).
% 1.46/1.29 thf(func_def_0, type, a: $tType).
% 1.46/1.29 thf(func_def_7, type, sK0: (a > a > a) > a).
% 1.46/1.29 thf(f11,plain,(
% 1.46/1.29 $false),
% 1.46/1.29 inference(subsumption_resolution,[status(thm)],[f9,f10])).
% 1.46/1.29 thf(f10,plain,(
% 1.46/1.29 ((^[Y0 : a > a > a]: (Y0 @ (sK0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (sK0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))) != sK0)),
% 1.46/1.29 inference(cnf_transformation,[status(thm)],[f8])).
% 1.46/1.29 thf(f8,plain,(
% 1.46/1.29 ((^[Y0 : a > a > a]: (Y0 @ (sK0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (sK0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))) != sK0) & ((^[Y0 : a > a > a]: (Y0 @ (sK0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (sK0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))) = sK0)),
% 1.46/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7])).
% 1.46/1.29 thf(f7,plain,(
% 1.46/1.29 ? [X0 : (a > a > a) > a] : (((^[Y0 : a > a > a]: (Y0 @ (X0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (X0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))) != X0) & ((^[Y0 : a > a > a]: (Y0 @ (X0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (X0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))) = X0)) => (((^[Y0 : a > a > a]: (Y0 @ (sK0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (sK0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))) != sK0) & ((^[Y0 : a > a > a]: (Y0 @ (sK0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (sK0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))) = sK0))),
% 1.46/1.29 introduced(definition,[],[choice_axiom])).
% 1.46/1.29 thf(f6,plain,(
% 1.46/1.29 ? [X0 : (a > a > a) > a] : (((^[Y0 : a > a > a]: (Y0 @ (X0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (X0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))) != X0) & ((^[Y0 : a > a > a]: (Y0 @ (X0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (X0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))) = X0))),
% 1.46/1.29 inference(ennf_transformation,[status(thm)],[f5])).
% 1.46/1.29 thf(f5,plain,(
% 1.46/1.29 ~! [X0 : (a > a > a) > a] : (((^[Y0 : a > a > a]: (Y0 @ (X0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (X0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))) = X0) => ((^[Y0 : a > a > a]: (Y0 @ (X0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (X0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))) = X0))),
% 1.46/1.29 inference(fool_elimination,[status(thm)],[f4])).
% 1.46/1.29 thf(f4,plain,(
% 1.46/1.29 ~! [X0 : (a > a > a) > a] : (((^[X1 : a > a > a] : (X1 @ (X0 @ (^[X2 : a, X3 : a] : (X2))) @ (X0 @ (^[X4 : a, X5 : a] : (X5))))) = X0) => (X0 = (^[X6 : a > a > a] : (X6 @ (X0 @ (^[X7 : a, X8 : a] : (X7))) @ (X0 @ (^[X9 : a, X10 : a] : (X10)))))))),
% 1.46/1.29 inference(rectify,[status(thm)],[f2])).
% 1.46/1.29 thf(f2,negated_conjecture,(
% 1.46/1.29 ~! [X0 : (a > a > a) > a] : (((^[X1 : a > a > a] : (X1 @ (X0 @ (^[X2 : a, X3 : a] : (X2))) @ (X0 @ (^[X2 : a, X3 : a] : (X3))))) = X0) => (X0 = (^[X1 : a > a > a] : (X1 @ (X0 @ (^[X2 : a, X3 : a] : (X2))) @ (X0 @ (^[X2 : a, X3 : a] : (X3)))))))),
% 1.46/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.46/1.29 thf(f1,conjecture,(
% 1.46/1.29 ! [X0 : (a > a > a) > a] : (((^[X1 : a > a > a] : (X1 @ (X0 @ (^[X2 : a, X3 : a] : (X2))) @ (X0 @ (^[X2 : a, X3 : a] : (X3))))) = X0) => (X0 = (^[X1 : a > a > a] : (X1 @ (X0 @ (^[X2 : a, X3 : a] : (X2))) @ (X0 @ (^[X2 : a, X3 : a] : (X3)))))))),
% 1.46/1.29 file('/export/starexec/sandbox/tmp/tmp.g4POOFKHLA/DTF2THF_11261.p',cTHM187_pme)).
% 1.46/1.29 thf(f9,plain,(
% 1.46/1.29 ((^[Y0 : a > a > a]: (Y0 @ (sK0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y1))))) @ (sK0 @ (^[Y1 : a]: ((^[Y2 : a]: (Y2))))))) = sK0)),
% 1.46/1.29 inference(cnf_transformation,[status(thm)],[f8])).
% 1.46/1.29 % SZS output end Proof for DTF2THF_11261
% 1.46/1.29 % (11454)------------------------------
% 1.46/1.29 % (11454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.46/1.29 % (11454)Termination reason: Refutation
% 1.46/1.29
% 1.46/1.29 % (11454)Memory used [KB]: 5500
% 1.46/1.29 % (11454)Time elapsed: 0.002 s
% 1.46/1.29 % (11454)------------------------------
% 1.46/1.29 % (11454)------------------------------
% 1.46/1.29 % (11448)Success in time 0.001 s
%------------------------------------------------------------------------------