%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV258^5 : 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 : n001.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 09:40:41 AM UTC 2026
% Result : Theorem 1.84s 1.51s
% Output : Refutation 1.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV258^5 : 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
% 0.13/0.32 % Computer : n001.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 12:43:35 EST 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.32 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.43 ---- Original DTF file ---
% 0.18/0.43 thf(spec,logic,$$dhol).
% 0.18/0.43 %------------------------------------------------------------------------------
% 0.18/0.43 % File : SEV258^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.43 % Domain : Set Theory (Sets of sets)
% 0.18/0.43 % Problem : TPS problem DISCRETE-TOPOLOGY
% 0.18/0.43 % Version : Especial.
% 0.18/0.43 % English : The discrete topology really is a topology.
% 0.18/0.43
% 0.18/0.43 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.43 % Source : [Bro09]
% 0.18/0.43 % Names : tps_0335 [Bro09]
% 0.18/0.43 % : DISCRETE-TOPOLOGY [TPS]
% 0.18/0.43
% 0.18/0.43 % Status : Theorem
% 0.18/0.43 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.15 v8.1.0, 0.00 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.18/0.43 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.18/0.43 % Number of atoms : 13 ( 4 equ; 0 cnn)
% 0.18/0.43 % Maximal formula atoms : 11 ( 13 avg)
% 0.18/0.43 % Number of connectives : 19 ( 1 ~; 0 |; 8 &; 5 @)
% 0.18/0.43 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.18/0.43 % Maximal formula depth : 11 ( 11 avg)
% 0.18/0.43 % Number of types : 2 ( 1 usr)
% 0.18/0.43 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.18/0.43 % Number of symbols : 3 ( 0 usr; 2 con; 0-2 aty)
% 0.18/0.43 % Number of variables : 13 ( 4 ^; 8 !; 1 ?; 13 :)
% 0.18/0.43 % SPC : TH0_THM_EQU_NAR
% 0.18/0.43
% 0.18/0.43 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.43 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.43 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.43 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.43 % : Polymorphic definitions expanded.
% 0.18/0.43 %------------------------------------------------------------------------------
% 0.18/0.43 thf(a_type,type,
% 0.18/0.43 a: $tType ).
% 0.18/0.43
% 0.18/0.43 thf(cDISCRETE_TOPOLOGY_pme,conjecture,
% 0.18/0.43 ( ! [R: a > $o] :
% 0.18/0.43 ( ( R
% 0.18/0.43 = ( ^ [Xx: a] : $false ) )
% 0.18/0.43 => $true )
% 0.18/0.43 & ! [R: a > $o] :
% 0.18/0.43 ( ( R
% 0.18/0.43 = ( ^ [Xx: a] : ~ $false ) )
% 0.18/0.43 => $true )
% 0.18/0.43 & ! [K: ( a > $o ) > $o,R: a > $o] :
% 0.18/0.43 ( ( ! [Xx: a > $o] :
% 0.18/0.43 ( ( K @ Xx )
% 0.18/0.43 => $true )
% 0.18/0.43 & ( R
% 0.18/0.43 = ( ^ [Xx: a] :
% 0.18/0.43 ? [S: a > $o] :
% 0.18/0.43 ( ( K @ S )
% 0.18/0.43 & ( S @ Xx ) ) ) ) )
% 0.18/0.43 => $true )
% 0.18/0.43 & ! [Y: a > $o,Z: a > $o,S: a > $o] :
% 0.18/0.43 ( ( $true
% 0.18/0.43 & $true
% 0.18/0.43 & ( S
% 0.18/0.43 = ( ^ [Xx: a] :
% 0.18/0.43 ( ( Y @ Xx )
% 0.18/0.43 & ( Z @ Xx ) ) ) ) )
% 0.18/0.43 => $true ) ) ).
% 0.18/0.43
% 0.18/0.43 %------------------------------------------------------------------------------
% 0.18/0.43 ------------------------
% 1.66/1.47 ---- Embedded in THF ---
% 1.66/1.47 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.66/1.47 %%% Generated on Tue Feb 24 12:43:36 EST 2026
% 1.66/1.47 %%% using '$$dhol' embedding, version 1.3.0.
% 1.66/1.47 %%% Logic specification used:
% 1.66/1.47 %%% thf(spec, logic, $$dhol).
% 1.66/1.47
% 1.66/1.47 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.IS22Hx3oyz/DTF2DTF13673.p
% 1.66/1.47 thf(a_type, type, a: $tType).
% 1.66/1.47 thf(cDISCRETE_TOPOLOGY_pme, conjecture, ((! [R:(a > $o)]: (((R = (^ [Xx:a]: ($false))) => $true))) & ((! [R:(a > $o)]: (((R = (^ [Xx:a]: ((~ ($false))))) => $true))) & ((! [K:((a > $o) > $o),R:(a > $o)]: ((((! [Xx:(a > $o)]: (((K @ Xx) => $true))) & (R = (^ [Xx:a]: ((? [S:(a > $o)]: (((K @ S) & (S @ Xx)))))))) => $true))) & (! [Y:(a > $o),Z:(a > $o),S:(a > $o)]: ((($true & ($true & (S = (^ [Xx:a]: (((Y @ Xx) & (Z @ Xx))))))) => $true))))))).
% 1.66/1.47 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.IS22Hx3oyz/DTF2DTF13673.p
% 1.66/1.47 ------------------------
% 1.66/1.48 ---- Cleaned THF ---
% 1.66/1.48 thf(a_type,type,
% 1.66/1.48 a: $tType ).
% 1.66/1.48
% 1.66/1.48 thf(cDISCRETE_TOPOLOGY_pme,conjecture,
% 1.66/1.48 ( ! [R: a > $o] :
% 1.66/1.48 ( ( R
% 1.66/1.48 = ( ^ [Xx: a] : $false ) )
% 1.66/1.48 => $true )
% 1.66/1.48 & ! [R: a > $o] :
% 1.66/1.48 ( ( R
% 1.66/1.48 = ( ^ [Xx: a] : ~ $false ) )
% 1.66/1.48 => $true )
% 1.66/1.48 & ! [K: ( a > $o ) > $o,R: a > $o] :
% 1.66/1.48 ( ( ! [Xx: a > $o] :
% 1.66/1.48 ( ( K @ Xx )
% 1.66/1.48 => $true )
% 1.66/1.48 & ( R
% 1.66/1.48 = ( ^ [Xx: a] :
% 1.66/1.48 ? [S: a > $o] :
% 1.66/1.48 ( ( K @ S )
% 1.66/1.48 & ( S @ Xx ) ) ) ) )
% 1.66/1.48 => $true )
% 1.66/1.48 & ! [Y: a > $o,Z: a > $o,S: a > $o] :
% 1.66/1.48 ( ( $true
% 1.66/1.48 & $true
% 1.66/1.48 & ( S
% 1.66/1.48 = ( ^ [Xx: a] :
% 1.66/1.48 ( ( Y @ Xx )
% 1.66/1.48 & ( Z @ Xx ) ) ) ) )
% 1.66/1.48 => $true ) ) ).
% 1.66/1.48 ------------------------
% 1.84/1.51 % (13774)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13673 for (2999ds/2Mi)
% 1.84/1.51 % (13773)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_13673 for (2999ds/27Mi)
% 1.84/1.51 % (13771)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13673 for (2999ds/183Mi)
% 1.84/1.51 % (13775)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_13673 for (2999ds/2Mi)
% 1.84/1.51 % (13777)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13673 for (2999ds/18Mi)
% 1.84/1.51 % (13775)Instruction limit reached!
% 1.84/1.51 % (13775)------------------------------
% 1.84/1.51 % (13775)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.51 % (13777)First to succeed.
% 1.84/1.51 % (13775)Termination reason: Unknown
% 1.84/1.51 % (13775)Termination phase: Property scanning
% 1.84/1.51
% 1.84/1.51 % (13775)Memory used [KB]: 895
% 1.84/1.51 % (13775)Time elapsed: 0.003 s
% 1.84/1.51 % (13775)Instructions burned: 2 (million)
% 1.84/1.51 % (13775)------------------------------
% 1.84/1.51 % (13775)------------------------------
% 1.84/1.51 % (13772)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_13673 for (2999ds/4Mi)
% 1.84/1.51 % (13776)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_13673 for (2999ds/275Mi)
% 1.84/1.51 % (13771)Also succeeded, but the first one will report.
% 1.84/1.51 % (13773)Also succeeded, but the first one will report.
% 1.84/1.51 % (13777)Refutation found. Thanks to Tanya!
% 1.84/1.51 % SZS status Theorem for DTF2THF_13673
% 1.84/1.51 % SZS output start Proof for DTF2THF_13673
% 1.84/1.51 tff(type_def_5, type, a: $tType).
% 1.84/1.51 tff(func_def_0, type, a: $tType).
% 1.84/1.51 fof(f8,plain,(
% 1.84/1.51 $false),
% 1.84/1.51 inference(cnf_transformation,[status(thm)],[f7])).
% 1.84/1.51 fof(f7,plain,(
% 1.84/1.51 $false),
% 1.84/1.51 inference(true_and_false_elimination,[status(thm)],[f6])).
% 1.84/1.51 fof(f6,plain,(
% 1.84/1.51 ~(! [X0 : sTfun(a,$o)] : (vLAM(a,$o,$false) = X0 => $true) & ! [X1 : sTfun(a,$o)] : (vLAM(a,$o,vAPP($o,$o,vNOT,$false)) = X1 => $true) & ! [X2 : sTfun(sTfun(a,$o),$o),X3 : sTfun(a,$o)] : ((! [X4 : sTfun(a,$o)] : (($true = vAPP(sTfun(a,$o),$o,X2,X4)) => $true) & vLAM(a,$o,vAPP(sTfun(sTfun(a,$o),$o),$o,vSIGMA(sTfun(a,$o)),vLAM(sTfun(a,$o),$o,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(sTfun(a,$o),$o,X2,db0(sTfun(a,$o)))),vAPP(a,$o,db0(sTfun(a,$o)),db1(a)))))) = X3) => $true) & ! [X5 : sTfun(a,$o),X6 : sTfun(a,$o),X7 : sTfun(a,$o)] : (($true & $true & vLAM(a,$o,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(a,$o,X6,db0(a))),vAPP(a,$o,X5,db0(a)))) = X7) => $true))),
% 1.84/1.51 inference(rectify,[status(thm)],[f5])).
% 1.84/1.51 fof(f5,plain,(
% 1.84/1.51 ~(! [X0 : sTfun(a,$o)] : (vLAM(a,$o,$false) = X0 => $true) & ! [X2 : sTfun(a,$o)] : (vLAM(a,$o,vAPP($o,$o,vNOT,$false)) = X2 => $true) & ! [X4 : sTfun(sTfun(a,$o),$o),X5 : sTfun(a,$o)] : ((! [X6 : sTfun(a,$o)] : (($true = vAPP(sTfun(a,$o),$o,X4,X6)) => $true) & vLAM(a,$o,vAPP(sTfun(sTfun(a,$o),$o),$o,vSIGMA(sTfun(a,$o)),vLAM(sTfun(a,$o),$o,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(sTfun(a,$o),$o,X4,db0(sTfun(a,$o)))),vAPP(a,$o,db0(sTfun(a,$o)),db1(a)))))) = X5) => $true) & ! [X9 : sTfun(a,$o),X10 : sTfun(a,$o),X11 : sTfun(a,$o)] : (($true & $true & vLAM(a,$o,vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(a,$o,X10,db0(a))),vAPP(a,$o,X9,db0(a)))) = X11) => $true))),
% 1.84/1.51 inference(fool_elimination,[status(thm)],[f4])).
% 1.84/1.51 fof(f4,plain,(
% 1.84/1.51 ~(! [X0 : sTfun(a,$o)] : ((^[X1 : a] : ($false)) = X0 => $true) & ! [X2 : sTfun(a,$o)] : (X2 = (^[X3 : a] : (~$false)) => $true) & ! [X4 : sTfun(sTfun(a,$o),$o),X5 : sTfun(a,$o)] : ((! [X6 : sTfun(a,$o)] : (vAPP(sTfun(a,$o),$o,X4,X6) => $true) & (^[X7 : a] : (? [X8 : sTfun(a,$o)] : (vAPP(a,$o,X8,X7) & vAPP(sTfun(a,$o),$o,X4,X8)))) = X5) => $true) & ! [X9 : sTfun(a,$o),X10 : sTfun(a,$o),X11 : sTfun(a,$o)] : (($true & $true & X11 = (^[X12 : a] : (vAPP(a,$o,X9,X12) & vAPP(a,$o,X10,X12)))) => $true))),
% 1.84/1.51 inference(rectify,[status(thm)],[f2])).
% 1.84/1.51 fof(f2,negated_conjecture,(
% 1.84/1.51 ~(! [X0 : sTfun(a,$o)] : ((^[X1 : a] : ($false)) = X0 => $true) & ! [X0 : sTfun(a,$o)] : (X0 = (^[X1 : a] : (~$false)) => $true) & ! [X2 : sTfun(sTfun(a,$o),$o),X0 : sTfun(a,$o)] : ((! [X1 : sTfun(a,$o)] : (vAPP(sTfun(a,$o),$o,X2,X1) => $true) & (^[X1 : a] : (? [X3 : sTfun(a,$o)] : (vAPP(a,$o,X3,X1) & vAPP(sTfun(a,$o),$o,X2,X3)))) = X0) => $true) & ! [X5 : sTfun(a,$o),X4 : sTfun(a,$o),X3 : sTfun(a,$o)] : (($true & $true & X3 = (^[X1 : a] : (vAPP(a,$o,X5,X1) & vAPP(a,$o,X4,X1)))) => $true))),
% 1.84/1.51 inference(negated_conjecture,[status(cth)],[f1])).
% 1.84/1.51 fof(f1,conjecture,(
% 1.84/1.51 ! [X0 : sTfun(a,$o)] : ((^[X1 : a] : ($false)) = X0 => $true) & ! [X0 : sTfun(a,$o)] : (X0 = (^[X1 : a] : (~$false)) => $true) & ! [X2 : sTfun(sTfun(a,$o),$o),X0 : sTfun(a,$o)] : ((! [X1 : sTfun(a,$o)] : (vAPP(sTfun(a,$o),$o,X2,X1) => $true) & (^[X1 : a] : (? [X3 : sTfun(a,$o)] : (vAPP(a,$o,X3,X1) & vAPP(sTfun(a,$o),$o,X2,X3)))) = X0) => $true) & ! [X5 : sTfun(a,$o),X4 : sTfun(a,$o),X3 : sTfun(a,$o)] : (($true & $true & X3 = (^[X1 : a] : (vAPP(a,$o,X5,X1) & vAPP(a,$o,X4,X1)))) => $true)),
% 1.84/1.51 file('/export/starexec/sandbox/tmp/tmp.IS22Hx3oyz/DTF2THF_13673.p',cDISCRETE_TOPOLOGY_pme)).
% 1.84/1.51 % SZS output end Proof for DTF2THF_13673
% 1.84/1.51 % (13777)------------------------------
% 1.84/1.51 % (13777)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.51 % (13777)Termination reason: Refutation
% 1.84/1.51
% 1.84/1.51 % (13777)Memory used [KB]: 5500
% 1.84/1.51 % (13777)Time elapsed: 0.003 s
% 1.84/1.51 % (13777)Instructions burned: 1 (million)
% 1.84/1.51 % (13777)------------------------------
% 1.84/1.51 % (13777)------------------------------
% 1.84/1.51 % (13770)Success in time 0.013 s
%------------------------------------------------------------------------------