%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV134^5 : 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 : n011.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 09:40:22 AM UTC 2026
% Result : Theorem 1.48s 1.26s
% Output : Refutation 1.48s
% 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 : 87 ( 37 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 125 ( 22 ~; 12 |; 16 &; 62 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 9 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 0 ^; 32 !; 12 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_4,type,
sK0: a > a > $o ).
thf(func_def_5,type,
sK1: a > $o ).
thf(func_def_6,type,
sK2: a ).
thf(f14,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f11,f13]) ).
thf(f13,plain,
( ( sK1 @ sK2 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( sK1 @ sK2 )
!= $true )
& ! [X3: a,X4: a] :
( ( ( sK1 @ X4 )
= $true )
| ( ( sK0 @ X3 @ X4 )
!= $true )
| ( ( sK1 @ X3 )
!= $true ) )
& ( ( sK1 @ sK2 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f9]) ).
thf(f9,plain,
( ? [X0: a > a > $o,X1: a > $o,X2: a] :
( ( ( X1 @ X2 )
!= $true )
& ! [X3: a,X4: a] :
( ( ( X1 @ X4 )
= $true )
| ( ( X0 @ X3 @ X4 )
!= $true )
| ( ( X1 @ X3 )
!= $true ) )
& ( ( X1 @ X2 )
= $true ) )
=> ( ( ( sK1 @ sK2 )
!= $true )
& ! [X4: a,X3: a] :
( ( ( sK1 @ X4 )
= $true )
| ( ( sK0 @ X3 @ X4 )
!= $true )
| ( ( sK1 @ X3 )
!= $true ) )
& ( ( sK1 @ sK2 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a > a > $o,X1: a > $o,X2: a] :
( ( ( X1 @ X2 )
!= $true )
& ! [X3: a,X4: a] :
( ( ( X1 @ X4 )
= $true )
| ( ( X0 @ X3 @ X4 )
!= $true )
| ( ( X1 @ X3 )
!= $true ) )
& ( ( X1 @ X2 )
= $true ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X1: a > a > $o,X0: a > $o,X2: a] :
( ( ( X0 @ X2 )
!= $true )
& ! [X4: a,X3: a] :
( ( ( X0 @ X3 )
= $true )
| ( ( X1 @ X4 @ X3 )
!= $true )
| ( ( X0 @ X4 )
!= $true ) )
& ( ( X0 @ X2 )
= $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X1: a > a > $o,X0: a > $o,X2: a] :
( ( ( X0 @ X2 )
!= $true )
& ( ( X0 @ X2 )
= $true )
& ! [X4: a,X3: a] :
( ( ( X0 @ X3 )
= $true )
| ( ( X1 @ X4 @ X3 )
!= $true )
| ( ( X0 @ X4 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X1: a > a > $o,X0: a > $o,X2: a] :
( ! [X4: a,X3: a] :
( ( ( ( X1 @ X4 @ X3 )
= $true )
& ( ( X0 @ X4 )
= $true ) )
=> ( ( X0 @ X3 )
= $true ) )
=> ( ( ( X0 @ X2 )
= $true )
=> ( ( X0 @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: a > a > $o,X2: a] :
( ! [X3: a,X4: a] :
( ( ( X1 @ X4 @ X3 )
& ( X0 @ X4 ) )
=> ( X0 @ X3 ) )
=> ( ( X0 @ X2 )
=> ( X0 @ X2 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: a > $o,X0: a > a > $o,X1: a] :
( ! [X4: a,X3: a] :
( ( ( X0 @ X3 @ X4 )
& ( X2 @ X3 ) )
=> ( X2 @ X4 ) )
=> ( ( X2 @ X1 )
=> ( X2 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X2: a > $o,X0: a > a > $o,X1: a] :
( ! [X4: a,X3: a] :
( ( ( X0 @ X3 @ X4 )
& ( X2 @ X3 ) )
=> ( X2 @ X4 ) )
=> ( ( X2 @ X1 )
=> ( X2 @ X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Jl5Uakcaj0/DTF2THF_21111.p',cTHM201_pme) ).
thf(f11,plain,
( ( sK1 @ sK2 )
= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV134^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n011.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:40:17 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.30/0.45 thf(spec,logic,$$dhol).
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % File : SEV134^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.45 % Domain : Set Theory (Relations)
% 0.30/0.45 % Problem : TPS problem THM201
% 0.30/0.45 % Version : Especial.
% 0.30/0.45 % English :
% 0.30/0.45
% 0.30/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.45 % Source : [Bro09]
% 0.30/0.45 % Names : tps_0123 [Bro09]
% 0.30/0.45 % : THM201 [TPS]
% 0.30/0.45
% 0.30/0.45 % Status : Theorem
% 0.30/0.45 % Rating : 0.00 v6.2.0, 0.17 v6.1.0, 0.00 v4.0.0
% 0.30/0.45 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.30/0.45 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.30/0.45 % Maximal formula atoms : 0 ( 0 avg)
% 0.30/0.45 % Number of connectives : 10 ( 0 ~; 0 |; 1 &; 6 @)
% 0.30/0.45 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 11 ( 11 avg)
% 0.30/0.45 % Number of types : 2 ( 1 usr)
% 0.30/0.45 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.30/0.45 % Number of variables : 5 ( 0 ^; 5 !; 0 ?; 5 :)
% 0.30/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.30/0.45
% 0.30/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.45 % : Polymorphic definitions expanded.
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 thf(a_type,type,
% 0.30/0.45 a: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(cTHM201_pme,conjecture,
% 0.30/0.45 ! [Xr: a > a > $o,Xx: a,Xx0: a > $o] :
% 0.30/0.45 ( ! [Xy: a,Xz: a] :
% 0.30/0.45 ( ( ( Xr @ Xy @ Xz )
% 0.30/0.45 & ( Xx0 @ Xy ) )
% 0.30/0.45 => ( Xx0 @ Xz ) )
% 0.30/0.45 => ( ( Xx0 @ Xx )
% 0.30/0.45 => ( Xx0 @ Xx ) ) ) ).
% 0.30/0.45
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 ------------------------
% 1.48/1.23 ---- Embedded in THF ---
% 1.48/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.23 %%% Generated on Tue Feb 24 12:40:18 EST 2026
% 1.48/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.23 %%% Logic specification used:
% 1.48/1.23 %%% thf(spec, logic, $$dhol).
% 1.48/1.23
% 1.48/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Jl5Uakcaj0/DTF2DTF21111.p
% See solution above
% 1.48/1.23 ------------------------
% 1.48/1.24 ---- Cleaned THF ---
% 1.48/1.25 thf(a_type,type,
% 1.48/1.25 a: $tType ).
% 1.48/1.25
% 1.48/1.25 thf(cTHM201_pme,conjecture,
% 1.48/1.25 ! [Xr: a > a > $o,Xx: a,Xx0: a > $o] :
% 1.48/1.25 ( ! [Xy: a,Xz: a] :
% 1.48/1.25 ( ( ( Xr @ Xy @ Xz )
% 1.48/1.25 & ( Xx0 @ Xy ) )
% 1.48/1.25 => ( Xx0 @ Xz ) )
% 1.48/1.25 => ( ( Xx0 @ Xx )
% 1.48/1.25 => ( Xx0 @ Xx ) ) ) ).
% 1.48/1.25 ------------------------
% 1.48/1.26 % (21213)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_21111 for (2999ds/2Mi)
% 1.48/1.26 % (21213)Instruction limit reached!
% 1.48/1.26 % (21213)------------------------------
% 1.48/1.26 % (21213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.26 % (21213)Termination reason: Unknown
% 1.48/1.26 % (21213)Termination phase: Saturation
% 1.48/1.26
% 1.48/1.26 % (21213)Memory used [KB]: 5373
% 1.48/1.26 % (21213)Time elapsed: 0.002 s
% 1.48/1.26 % (21213)Instructions burned: 2 (million)
% 1.48/1.26 % (21213)------------------------------
% 1.48/1.26 % (21213)------------------------------
% 1.48/1.26 % (21214)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_21111 for (2999ds/275Mi)
% 1.48/1.26 % (21214)First to succeed.
% 1.48/1.26 % (21214)Refutation found. Thanks to Tanya!
% 1.48/1.26 % SZS status Theorem for DTF2THF_21111
% 1.48/1.26 % SZS output start Proof for DTF2THF_21111
% 1.48/1.26 thf(type_def_5, type, a: $tType).
% 1.48/1.26 thf(func_def_0, type, a: $tType).
% 1.48/1.26 thf(func_def_4, type, sK0: a > a > $o).
% 1.48/1.26 thf(func_def_5, type, sK1: a > $o).
% 1.48/1.26 thf(func_def_6, type, sK2: a).
% 1.48/1.26 thf(f14,plain,(
% 1.48/1.26 $false),
% 1.48/1.26 inference(subsumption_resolution,[status(thm)],[f11,f13])).
% 1.48/1.26 thf(f13,plain,(
% 1.48/1.26 ((sK1 @ sK2) != $true)),
% 1.48/1.26 inference(cnf_transformation,[status(thm)],[f10])).
% 1.48/1.26 thf(f10,plain,(
% 1.48/1.26 ((sK1 @ sK2) != $true) & ! [X3 : a,X4 : a] : (((sK1 @ X4) = $true) | ((sK0 @ X3 @ X4) != $true) | ((sK1 @ X3) != $true)) & ((sK1 @ sK2) = $true)),
% 1.48/1.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f9])).
% 1.48/1.26 thf(f9,plain,(
% 1.48/1.26 ? [X0 : a > a > $o,X1 : a > $o,X2 : a] : (((X1 @ X2) != $true) & ! [X3 : a,X4 : a] : (((X1 @ X4) = $true) | ((X0 @ X3 @ X4) != $true) | ((X1 @ X3) != $true)) & ((X1 @ X2) = $true)) => (((sK1 @ sK2) != $true) & ! [X4 : a,X3 : a] : (((sK1 @ X4) = $true) | ((sK0 @ X3 @ X4) != $true) | ((sK1 @ X3) != $true)) & ((sK1 @ sK2) = $true))),
% 1.48/1.26 introduced(definition,[],[choice_axiom])).
% 1.48/1.26 thf(f8,plain,(
% 1.48/1.26 ? [X0 : a > a > $o,X1 : a > $o,X2 : a] : (((X1 @ X2) != $true) & ! [X3 : a,X4 : a] : (((X1 @ X4) = $true) | ((X0 @ X3 @ X4) != $true) | ((X1 @ X3) != $true)) & ((X1 @ X2) = $true))),
% 1.48/1.26 inference(rectify,[status(thm)],[f7])).
% 1.48/1.26 thf(f7,plain,(
% 1.48/1.26 ? [X1 : a > a > $o,X0 : a > $o,X2 : a] : (((X0 @ X2) != $true) & ! [X4 : a,X3 : a] : (((X0 @ X3) = $true) | ((X1 @ X4 @ X3) != $true) | ((X0 @ X4) != $true)) & ((X0 @ X2) = $true))),
% 1.48/1.26 inference(flattening,[status(thm)],[f6])).
% 1.48/1.26 thf(f6,plain,(
% 1.48/1.26 ? [X1 : a > a > $o,X0 : a > $o,X2 : a] : ((((X0 @ X2) != $true) & ((X0 @ X2) = $true)) & ! [X4 : a,X3 : a] : (((X0 @ X3) = $true) | (((X1 @ X4 @ X3) != $true) | ((X0 @ X4) != $true))))),
% 1.48/1.26 inference(ennf_transformation,[status(thm)],[f5])).
% 1.48/1.26 thf(f5,plain,(
% 1.48/1.26 ~! [X1 : a > a > $o,X0 : a > $o,X2 : a] : (! [X4 : a,X3 : a] : ((((X1 @ X4 @ X3) = $true) & ((X0 @ X4) = $true)) => ((X0 @ X3) = $true)) => (((X0 @ X2) = $true) => ((X0 @ X2) = $true)))),
% 1.48/1.26 inference(fool_elimination,[status(thm)],[f4])).
% 1.48/1.26 thf(f4,plain,(
% 1.48/1.26 ~! [X0 : a > $o,X1 : a > a > $o,X2 : a] : (! [X3 : a,X4 : a] : (((X1 @ X4 @ X3) & (X0 @ X4)) => (X0 @ X3)) => ((X0 @ X2) => (X0 @ X2)))),
% 1.48/1.26 inference(rectify,[status(thm)],[f2])).
% 1.48/1.26 thf(f2,negated_conjecture,(
% 1.48/1.26 ~! [X2 : a > $o,X0 : a > a > $o,X1 : a] : (! [X4 : a,X3 : a] : (((X0 @ X3 @ X4) & (X2 @ X3)) => (X2 @ X4)) => ((X2 @ X1) => (X2 @ X1)))),
% 1.48/1.26 inference(negated_conjecture,[status(cth)],[f1])).
% 1.48/1.26 thf(f1,conjecture,(
% 1.48/1.26 ! [X2 : a > $o,X0 : a > a > $o,X1 : a] : (! [X4 : a,X3 : a] : (((X0 @ X3 @ X4) & (X2 @ X3)) => (X2 @ X4)) => ((X2 @ X1) => (X2 @ X1)))),
% 1.48/1.26 file('/export/starexec/sandbox/tmp/tmp.Jl5Uakcaj0/DTF2THF_21111.p',cTHM201_pme)).
% 1.48/1.26 thf(f11,plain,(
% 1.48/1.26 ((sK1 @ sK2) = $true)),
% 1.48/1.26 inference(cnf_transformation,[status(thm)],[f10])).
% 1.48/1.26 % SZS output end Proof for DTF2THF_21111
% 1.48/1.26 % (21214)------------------------------
% 1.48/1.26 % (21214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.26 % (21214)Termination reason: Refutation
% 1.48/1.26
% 1.48/1.26 % (21214)Memory used [KB]: 5500
% 1.48/1.26 % (21214)Time elapsed: 0.002 s
% 1.48/1.26 % (21214)Instructions burned: 1 (million)
% 1.48/1.26 % (21214)------------------------------
% 1.48/1.26 % (21214)------------------------------
% 1.48/1.26 % (21208)Success in time 0.012 s
%------------------------------------------------------------------------------