%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : CSR115+63 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 : Thu Jul 24 11:19:40 AM UTC 2025
% Result : Theorem 7.28s 1.41s
% Output : CNFRefutation 7.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 64 ( 31 unt; 0 def)
% Number of atoms : 431 ( 0 equ)
% Maximal formula atoms : 271 ( 6 avg)
% Number of connectives : 430 ( 63 ~; 60 |; 303 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 271 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 22 usr; 1 prp; 0-10 aty)
% Number of functors : 72 ( 72 usr; 69 con; 0-3 aty)
% Number of variables : 54 ( 3 sgn 10 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(synth_qa07_007_mira_wp_471,plain,
? [X0,X1,X2,X3,X4,X5,X6] :
( attr(X0,X1)
& attr(X3,X2)
& attr(X5,X6)
& obj(X4,X0)
& sub(X1,name_1_1)
& sub(X0,firma_1_1)
& sub(X2,name_1_1)
& sub(X6,jahr__1_1)
& val(X1,bmw_0)
& val(X2,bmw_0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',synth_qa07_007_mira_wp_471) ).
fof(synth_qa07_007_mira_wp_471_negated,plain,
~ ? [X0,X1,X2,X3,X4,X5,X6] :
( attr(X0,X1)
& attr(X3,X2)
& attr(X5,X6)
& obj(X4,X0)
& sub(X1,name_1_1)
& sub(X0,firma_1_1)
& sub(X2,name_1_1)
& sub(X6,jahr__1_1)
& val(X1,bmw_0)
& val(X2,bmw_0) ),
inference(negate_conjecture,[status(cth)],[synth_qa07_007_mira_wp_471]) ).
cnf(10360,plain,
( ~ sub(X0,firma_1_1)
| ~ sub(X1,name_1_1)
| ~ sub(X2,name_1_1)
| ~ sub(X3,jahr__1_1)
| ~ obj(X4,X0)
| ~ attr(X0,X1)
| ~ attr(X5,X2)
| ~ attr(X6,X3)
| ~ val(X1,bmw_0)
| ~ val(X2,bmw_0) ),
inference(cnf,[status(esa)],[synth_qa07_007_mira_wp_471_negated]) ).
cnf(l0,plain,
( ~ sub(c703,firma_1_1)
| ~ sub(sK61(bmw_0,c703),name_1_1)
| ~ sub(sK61(bmw_0,c703),name_1_1)
| ~ sub(c652,jahr__1_1)
| ~ obj(sK55(sK58(c703,firma_1_1),c703,firma_1_1),c703)
| ~ attr(c703,sK61(bmw_0,c703))
| ~ attr(c703,sK61(bmw_0,c703))
| ~ attr(c649,c652)
| ~ val(sK61(bmw_0,c703),bmw_0)
| ~ val(sK61(bmw_0,c703),bmw_0) ),
inference(instantiation,[status(thm)],[10360]) ).
fof(name_rel__attr_val_name_1_1,plain,
! [X0,X1] :
( name(X1,X0)
=> ? [X2] :
( attr(X1,X2)
& sub(X2,name_1_1)
& val(X2,X0) ) ),
file('Axioms/CSR004+0.ax',name_rel__attr_val_name_1_1) ).
cnf(343,plain,
( ~ name(X0,X1)
| attr(X0,sK61(X1,X0)) ),
inference(cnf,[status(esa)],[name_rel__attr_val_name_1_1]) ).
cnf(l10,plain,
( ~ name(c703,bmw_0)
| attr(c703,sK61(bmw_0,c703)) ),
inference(instantiation,[status(thm)],[343]) ).
cnf(344,plain,
( ~ name(X0,X1)
| sub(sK61(X1,X0),name_1_1) ),
inference(cnf,[status(esa)],[name_rel__attr_val_name_1_1]) ).
cnf(l11,plain,
( ~ name(c703,bmw_0)
| sub(sK61(bmw_0,c703),name_1_1) ),
inference(instantiation,[status(thm)],[344]) ).
cnf(l15,plain,
( ~ name(c703,bmw_0)
| sub(sK61(bmw_0,c703),name_1_1) ),
inference(instantiation,[status(thm)],[344]) ).
cnf(l5,plain,
( ~ name(c703,bmw_0)
| attr(c703,sK61(bmw_0,c703)) ),
inference(instantiation,[status(thm)],[343]) ).
fof(attr_val_name_1_1__name_rel,plain,
! [X0,X1,X2] :
( ( attr(X2,X0)
& sub(X0,name_1_1)
& val(X0,X1) )
=> name(X2,X1) ),
file('Axioms/CSR004+0.ax',attr_val_name_1_1__name_rel) ).
cnf(346,plain,
( ~ sub(X0,name_1_1)
| ~ attr(X1,X0)
| ~ val(X0,X2)
| name(X1,X2) ),
inference(cnf,[status(esa)],[attr_val_name_1_1__name_rel]) ).
cnf(l45,plain,
( ~ sub(c704,name_1_1)
| ~ attr(c703,c704)
| ~ val(c704,bmw_0)
| name(c703,bmw_0) ),
inference(instantiation,[status(thm)],[346]) ).
cnf(l62,plain,
( ~ sub(c704,name_1_1)
| ~ attr(c703,c704)
| ~ val(c704,bmw_0)
| name(c703,bmw_0) ),
inference(instantiation,[status(thm)],[346]) ).
fof(ave07_era5_synth_qa07_007_mira_wp_471,plain,
( sub(c631,bau_1_1)
& attch(c634,c631)
& sub(c634,goggomobil_1_1)
& sub(c640,man_1_1)
& attr(c649,c650)
& attr(c649,c651)
& attr(c649,c652)
& sub(c650,tag_1_1)
& val(c650,c646)
& sub(c651,monat_1_1)
& val(c651,c647)
& sub(c652,jahr__1_1)
& val(c652,c648)
& quant_p3(c658,c654,jahr__1_1)
& quant_p3(c663,c659,monat_1_1)
& attr(c703,c704)
& sub(c703,firma_1_1)
& sub(c704,name_1_1)
& val(c704,bmw_0)
& sub(c705,firma_1_1)
& sub(c711,glas_1_1)
& attr(c713,c714)
& sub(c713,mensch_1_1)
& sub(c714,eigenname_1_1)
& val(c714,hans_0)
& tupl_p10(c745,c631,c640,c649,c658,c663,c703,c705,c713,c711)
& sort(c631,d)
& card(c631,int1)
& etype(c631,int0)
& fact(c631,real)
& gener(c631,sp)
& quant(c631,one)
& refer(c631,det)
& varia(c631,con)
& sort(bau_1_1,d)
& card(bau_1_1,int1)
& etype(bau_1_1,int0)
& fact(bau_1_1,real)
& gener(bau_1_1,ge)
& quant(bau_1_1,one)
& refer(bau_1_1,refer_c)
& varia(bau_1_1,varia_c)
& sort(c634,o)
& card(c634,int1)
& etype(c634,int0)
& fact(c634,real)
& gener(c634,sp)
& quant(c634,one)
& refer(c634,det)
& varia(c634,con)
& sort(goggomobil_1_1,o)
& card(goggomobil_1_1,int1)
& etype(goggomobil_1_1,int0)
& fact(goggomobil_1_1,real)
& gener(goggomobil_1_1,ge)
& quant(goggomobil_1_1,one)
& refer(goggomobil_1_1,refer_c)
& varia(goggomobil_1_1,varia_c)
& sort(c640,d)
& card(c640,int1)
& etype(c640,int0)
& fact(c640,real)
& gener(c640,ge)
& quant(c640,one)
& refer(c640,refer_c)
& varia(c640,varia_c)
& sort(man_1_1,d)
& card(man_1_1,int1)
& etype(man_1_1,int0)
& fact(man_1_1,real)
& gener(man_1_1,ge)
& quant(man_1_1,one)
& refer(man_1_1,refer_c)
& varia(man_1_1,varia_c)
& sort(c649,t)
& card(c649,int1)
& etype(c649,int0)
& fact(c649,real)
& gener(c649,sp)
& quant(c649,one)
& refer(c649,det)
& varia(c649,con)
& sort(c650,me)
& sort(c650,oa)
& sort(c650,ta)
& card(c650,card_c)
& etype(c650,etype_c)
& fact(c650,real)
& gener(c650,sp)
& quant(c650,quant_c)
& refer(c650,refer_c)
& varia(c650,varia_c)
& sort(c651,me)
& sort(c651,oa)
& sort(c651,ta)
& card(c651,card_c)
& etype(c651,etype_c)
& fact(c651,real)
& gener(c651,sp)
& quant(c651,quant_c)
& refer(c651,refer_c)
& varia(c651,varia_c)
& sort(c652,me)
& sort(c652,oa)
& sort(c652,ta)
& card(c652,card_c)
& etype(c652,etype_c)
& fact(c652,real)
& gener(c652,sp)
& quant(c652,quant_c)
& refer(c652,refer_c)
& varia(c652,varia_c)
& sort(tag_1_1,me)
& sort(tag_1_1,oa)
& sort(tag_1_1,ta)
& card(tag_1_1,card_c)
& etype(tag_1_1,etype_c)
& fact(tag_1_1,real)
& gener(tag_1_1,ge)
& quant(tag_1_1,quant_c)
& refer(tag_1_1,refer_c)
& varia(tag_1_1,varia_c)
& sort(c646,nu)
& card(c646,int30)
& sort(monat_1_1,me)
& sort(monat_1_1,oa)
& sort(monat_1_1,ta)
& card(monat_1_1,card_c)
& etype(monat_1_1,etype_c)
& fact(monat_1_1,real)
& gener(monat_1_1,ge)
& quant(monat_1_1,quant_c)
& refer(monat_1_1,refer_c)
& varia(monat_1_1,varia_c)
& sort(c647,nu)
& card(c647,int6)
& sort(jahr__1_1,me)
& sort(jahr__1_1,oa)
& sort(jahr__1_1,ta)
& card(jahr__1_1,card_c)
& etype(jahr__1_1,etype_c)
& fact(jahr__1_1,real)
& gener(jahr__1_1,ge)
& quant(jahr__1_1,quant_c)
& refer(jahr__1_1,refer_c)
& varia(jahr__1_1,varia_c)
& sort(c648,nu)
& card(c648,int1969)
& sort(c658,m)
& sort(c658,ta)
& card(c658,card_c)
& etype(c658,etype_c)
& fact(c658,real)
& gener(c658,gener_c)
& quant(c658,quant_c)
& refer(c658,refer_c)
& varia(c658,varia_c)
& sort(c654,nu)
& card(c654,int2)
& sort(c663,m)
& sort(c663,ta)
& card(c663,card_c)
& etype(c663,etype_c)
& fact(c663,real)
& gener(c663,gener_c)
& quant(c663,quant_c)
& refer(c663,refer_c)
& varia(c663,varia_c)
& sort(c659,nu)
& card(c659,int6)
& sort(c703,d)
& sort(c703,io)
& card(c703,int1)
& etype(c703,int0)
& fact(c703,real)
& gener(c703,sp)
& quant(c703,one)
& refer(c703,det)
& varia(c703,con)
& sort(c704,na)
& card(c704,int1)
& etype(c704,int0)
& fact(c704,real)
& gener(c704,sp)
& quant(c704,one)
& refer(c704,indet)
& varia(c704,varia_c)
& sort(firma_1_1,d)
& sort(firma_1_1,io)
& card(firma_1_1,int1)
& etype(firma_1_1,int0)
& fact(firma_1_1,real)
& gener(firma_1_1,ge)
& quant(firma_1_1,one)
& refer(firma_1_1,refer_c)
& varia(firma_1_1,varia_c)
& sort(name_1_1,na)
& card(name_1_1,int1)
& etype(name_1_1,int0)
& fact(name_1_1,real)
& gener(name_1_1,ge)
& quant(name_1_1,one)
& refer(name_1_1,refer_c)
& varia(name_1_1,varia_c)
& sort(bmw_0,fe)
& sort(c705,d)
& sort(c705,io)
& card(c705,int1)
& etype(c705,int0)
& fact(c705,real)
& gener(c705,sp)
& quant(c705,one)
& refer(c705,det)
& varia(c705,con)
& sort(c711,s)
& card(c711,int1)
& etype(c711,int0)
& fact(c711,real)
& gener(c711,gener_c)
& quant(c711,one)
& refer(c711,refer_c)
& varia(c711,varia_c)
& sort(glas_1_1,s)
& card(glas_1_1,int1)
& etype(glas_1_1,int0)
& fact(glas_1_1,real)
& gener(glas_1_1,ge)
& quant(glas_1_1,one)
& refer(glas_1_1,refer_c)
& varia(glas_1_1,varia_c)
& sort(c713,d)
& card(c713,int1)
& etype(c713,int0)
& fact(c713,real)
& gener(c713,sp)
& quant(c713,one)
& refer(c713,det)
& varia(c713,con)
& sort(c714,na)
& card(c714,int1)
& etype(c714,int0)
& fact(c714,real)
& gener(c714,sp)
& quant(c714,one)
& refer(c714,indet)
& varia(c714,varia_c)
& sort(mensch_1_1,d)
& card(mensch_1_1,int1)
& etype(mensch_1_1,int0)
& fact(mensch_1_1,real)
& gener(mensch_1_1,ge)
& quant(mensch_1_1,one)
& refer(mensch_1_1,refer_c)
& varia(mensch_1_1,varia_c)
& sort(eigenname_1_1,na)
& card(eigenname_1_1,int1)
& etype(eigenname_1_1,int0)
& fact(eigenname_1_1,real)
& gener(eigenname_1_1,ge)
& quant(eigenname_1_1,one)
& refer(eigenname_1_1,refer_c)
& varia(eigenname_1_1,varia_c)
& sort(hans_0,fe)
& sort(c745,ent)
& card(c745,card_c)
& etype(c745,etype_c)
& fact(c745,real)
& gener(c745,gener_c)
& quant(c745,quant_c)
& refer(c745,refer_c)
& varia(c745,varia_c) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ave07_era5_synth_qa07_007_mira_wp_471) ).
cnf(10367,plain,
attr(c649,c652),
inference(cnf,[status(esa)],[ave07_era5_synth_qa07_007_mira_wp_471]) ).
cnf(l9,plain,
attr(c649,c652),
inference(instantiation,[status(thm)],[10367]) ).
cnf(10372,plain,
sub(c652,jahr__1_1),
inference(cnf,[status(esa)],[ave07_era5_synth_qa07_007_mira_wp_471]) ).
cnf(l1,plain,
sub(c652,jahr__1_1),
inference(instantiation,[status(thm)],[10372]) ).
cnf(10377,plain,
sub(c703,firma_1_1),
inference(cnf,[status(esa)],[ave07_era5_synth_qa07_007_mira_wp_471]) ).
cnf(l3,plain,
sub(c703,firma_1_1),
inference(instantiation,[status(thm)],[10377]) ).
cnf(l39,plain,
( ~ sub(c704,name_1_1)
| ~ attr(c703,c704)
| ~ val(c704,bmw_0)
| name(c703,bmw_0) ),
inference(instantiation,[status(thm)],[346]) ).
cnf(10378,plain,
sub(c704,name_1_1),
inference(cnf,[status(esa)],[ave07_era5_synth_qa07_007_mira_wp_471]) ).
cnf(l63,plain,
sub(c704,name_1_1),
inference(instantiation,[status(thm)],[10378]) ).
cnf(10376,plain,
attr(c703,c704),
inference(cnf,[status(esa)],[ave07_era5_synth_qa07_007_mira_wp_471]) ).
cnf(l64,plain,
attr(c703,c704),
inference(instantiation,[status(thm)],[10376]) ).
cnf(l98,plain,
sub(c704,name_1_1),
inference(instantiation,[status(thm)],[10378]) ).
cnf(l28,plain,
( ~ sub(c704,name_1_1)
| ~ attr(c703,c704)
| ~ val(c704,bmw_0)
| name(c703,bmw_0) ),
inference(instantiation,[status(thm)],[346]) ).
cnf(l41,plain,
attr(c703,c704),
inference(instantiation,[status(thm)],[10376]) ).
cnf(345,plain,
( ~ name(X0,X1)
| val(sK61(X1,X0),X1) ),
inference(cnf,[status(esa)],[name_rel__attr_val_name_1_1]) ).
cnf(l13,plain,
( ~ name(c703,bmw_0)
| val(sK61(bmw_0,c703),bmw_0) ),
inference(instantiation,[status(thm)],[345]) ).
cnf(10379,plain,
val(c704,bmw_0),
inference(cnf,[status(esa)],[ave07_era5_synth_qa07_007_mira_wp_471]) ).
cnf(l94,plain,
val(c704,bmw_0),
inference(instantiation,[status(thm)],[10379]) ).
cnf(l72,plain,
attr(c703,c704),
inference(instantiation,[status(thm)],[10376]) ).
cnf(l171,plain,
val(c704,bmw_0),
inference(instantiation,[status(thm)],[10379]) ).
cnf(l69,plain,
val(c704,bmw_0),
inference(instantiation,[status(thm)],[10379]) ).
fof(sub__bezeichnen_1_1_als,plain,
! [X0,X1,X2] :
( ( arg1(X0,X1)
& arg2(X0,X2)
& subr(X0,sub_0) )
=> ? [X3,X4,X5] :
( arg1(X4,X1)
& arg2(X4,X5)
& hsit(X0,X3)
& mcont(X3,X4)
& obj(X3,X1)
& sub(X5,X2)
& subr(X4,rprs_0)
& subs(X3,bezeichnen_1_1) ) ),
file('Axioms/CSR004+0.ax',sub__bezeichnen_1_1_als) ).
cnf(304,plain,
( ~ arg1(X0,X1)
| ~ arg2(X0,X2)
| ~ subr(X0,sub_0)
| obj(sK55(X0,X1,X2),X1) ),
inference(cnf,[status(esa)],[sub__bezeichnen_1_1_als]) ).
cnf(l65,plain,
( ~ arg1(sK58(c703,firma_1_1),c703)
| ~ arg2(sK58(c703,firma_1_1),firma_1_1)
| ~ subr(sK58(c703,firma_1_1),sub_0)
| obj(sK55(sK58(c703,firma_1_1),c703,firma_1_1),c703) ),
inference(instantiation,[status(thm)],[304]) ).
fof(sub__sub_0_expansion,plain,
! [X0,X1] :
( sub(X0,X1)
=> ? [X2] :
( arg1(X2,X0)
& arg2(X2,X1)
& subr(X2,sub_0) ) ),
file('Axioms/CSR004+0.ax',sub__sub_0_expansion) ).
cnf(310,plain,
( ~ sub(X0,X1)
| subr(sK58(X0,X1),sub_0) ),
inference(cnf,[status(esa)],[sub__sub_0_expansion]) ).
cnf(l109,plain,
( ~ sub(c703,firma_1_1)
| subr(sK58(c703,firma_1_1),sub_0) ),
inference(instantiation,[status(thm)],[310]) ).
cnf(l53,plain,
sub(c704,name_1_1),
inference(instantiation,[status(thm)],[10378]) ).
cnf(309,plain,
( ~ sub(X0,X1)
| arg2(sK58(X0,X1),X1) ),
inference(cnf,[status(esa)],[sub__sub_0_expansion]) ).
cnf(l71,plain,
( ~ sub(c703,firma_1_1)
| arg2(sK58(c703,firma_1_1),firma_1_1) ),
inference(instantiation,[status(thm)],[309]) ).
cnf(l4,plain,
( ~ name(c703,bmw_0)
| val(sK61(bmw_0,c703),bmw_0) ),
inference(instantiation,[status(thm)],[345]) ).
cnf(l59,plain,
attr(c703,c704),
inference(instantiation,[status(thm)],[10376]) ).
cnf(l68,plain,
val(c704,bmw_0),
inference(instantiation,[status(thm)],[10379]) ).
cnf(l37,plain,
( ~ sub(c704,name_1_1)
| ~ attr(c703,c704)
| ~ val(c704,bmw_0)
| name(c703,bmw_0) ),
inference(instantiation,[status(thm)],[346]) ).
cnf(l60,plain,
val(c704,bmw_0),
inference(instantiation,[status(thm)],[10379]) ).
cnf(l61,plain,
sub(c704,name_1_1),
inference(instantiation,[status(thm)],[10378]) ).
cnf(l42,plain,
( ~ sub(c704,name_1_1)
| ~ attr(c703,c704)
| ~ val(c704,bmw_0)
| name(c703,bmw_0) ),
inference(instantiation,[status(thm)],[346]) ).
cnf(l43,plain,
attr(c703,c704),
inference(instantiation,[status(thm)],[10376]) ).
cnf(l58,plain,
attr(c703,c704),
inference(instantiation,[status(thm)],[10376]) ).
cnf(308,plain,
( ~ sub(X0,X1)
| arg1(sK58(X0,X1),X0) ),
inference(cnf,[status(esa)],[sub__sub_0_expansion]) ).
cnf(l70,plain,
( ~ sub(c703,firma_1_1)
| arg1(sK58(c703,firma_1_1),c703) ),
inference(instantiation,[status(thm)],[308]) ).
cnf(l91,plain,
sub(c704,name_1_1),
inference(instantiation,[status(thm)],[10378]) ).
cnf(l44,plain,
val(c704,bmw_0),
inference(instantiation,[status(thm)],[10379]) ).
cnf(l99,plain,
sub(c704,name_1_1),
inference(instantiation,[status(thm)],[10378]) ).
cnf(l139,plain,
sub(c703,firma_1_1),
inference(instantiation,[status(thm)],[10377]) ).
cnf(l117,plain,
sub(c703,firma_1_1),
inference(instantiation,[status(thm)],[10377]) ).
cnf(l143,plain,
sub(c703,firma_1_1),
inference(instantiation,[status(thm)],[10377]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l10,l11,l15,l5,l45,l62,l9,l1,l3,l39,l63,l64,l98,l28,l41,l13,l94,l72,l171,l69,l65,l109,l53,l71,l4,l59,l68,l37,l60,l61,l42,l43,l58,l70,l91,l44,l99,l139,l117,l143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : CSR115+63 : TPTP v9.0.0. Released v4.0.0.
% 0.09/0.14 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.36 % Computer : n018.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun Jul 20 08:20:04 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.21/0.50 % launching worker at depth: 2
% 0.21/0.50 % launching worker at depth: 3
% 0.21/0.50 % launching worker at depth: 4
% 0.21/0.50 % launching worker at depth: 5
% 0.21/0.50 % launching worker at depth: 6
% 0.21/0.50 % launching worker at depth: 1
% 0.21/0.50 % launching worker at depth: 7
% 0.21/0.50 % launching worker at depth: 8
% 0.21/0.52 % launching worker at depth: 9
% 1.30/0.67 % launching worker at depth: 10
% 7.28/1.41 % SZS status Theorem for theBenchmark
% 7.28/1.41 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------