%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWV897-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n006.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 Apr 9 09:31:52 PM UTC 2025
% Result : Unsatisfiable 27.91s 11.81s
% Output : CNFRefutation 27.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 10 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 25 ( 24 usr; 1 prp; 0-4 aty)
% Number of functors : 58 ( 58 usr; 20 con; 0-10 aty)
% Number of variables : 6 ( 6 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_Natural_Oevaln > c_Fun_Oinj__on > c_lessequals > c_Hoare__Mirabelle_Otriple__valid > c_Hoare__Mirabelle_Ohoare__valids > c_Hoare__Mirabelle_Ohoare__derivs > hBOOL > class_Ring__and__Field_Oidom > class_Orderings_Otop > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > class_Orderings_Obot > class_OrderedGroup_Opordered__ab__group__add > class_OrderedGroup_Olordered__ab__group__add > class_OrderedGroup_Ogroup__add > class_OrderedGroup_Oab__group__add > class_Lattices_Oupper__semilattice > class_Lattices_Olattice > class_Lattices_Obounded__lattice > class_Int_Onumber__ring > class_HOL_Oord > class_HOL_Ominus > c_Com_OWT > c_Com_Ocom_Ocom__rec > c_Com_Ocom_Ocom__case > c_Fun_Ofcomp > c_Fun_Ocomp > c_COMBS > c_COMBC > c_COMBB > c_Set_Ovimage > c_Set_Oimage > c_Natural_Osko__Natural__Xevaln__elim__cases__6__1 > c_Hoare__Mirabelle_Otriple_Otriple__rec > c_Hoare__Mirabelle_Otriple_Otriple__case > c_Set_Oinsert > c_Lattices_Oupper__semilattice__class_Osup > c_HOL_Ominus__class_Ominus > c_Com_Ocom_OLocal > c_Com_Ocom_OCond > c_Com_Ocom_OCall > tc_fun > hAPP > c_OrderedGroup_Olordered__ab__group__add__class_Opprt > c_Option_Ooption_OSome > c_Com_Ocom_OWhile > c_Com_Ocom_OSemi > c_Com_Ocom_OAss > #nlpp > tc_Option_Ooption > tc_Hoare__Mirabelle_Otriple > c_in > c_fequal > c_Suc > c_Orderings_Otop__class_Otop > c_Orderings_Obot__class_Obot > c_Option_Othe > c_Option_Ooption_ONone > c_Hoare__Mirabelle_Otriple_Otriple > c_Hoare__Mirabelle_OMGT > c_HOL_Ozero__class_Ozero > c_Fun_Oid > v_xa > v_x > v_pn > v_g > v_f > v_c > v_Procs > v_G > tc_nat > tc_bool > tc_Com_Ostate > tc_Com_Opname > tc_Com_Ocom > t_c > t_b > t_a > c_Natural_Oevalc > c_Com_Ocom_OSKIP > c_Com_Ocom_OBODY > c_Com_Obody
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(tc_Com_Ostate,type,
tc_Com_Ostate: $i ).
tff(v_x,type,
v_x: $i ).
tff(c_Set_Oinsert,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
tff(class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $i > $o ).
tff(class_HOL_Ominus,type,
class_HOL_Ominus: $i > $o ).
tff(c_COMBC,type,
c_COMBC: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_Orderings_Otop__class_Otop,type,
c_Orderings_Otop__class_Otop: $i > $i ).
tff(c_fequal,type,
c_fequal: $i > $i ).
tff(c_OrderedGroup_Olordered__ab__group__add__class_Opprt,type,
c_OrderedGroup_Olordered__ab__group__add__class_Opprt: ( $i * $i ) > $i ).
tff(v_c,type,
v_c: $i ).
tff(v_G,type,
v_G: $i ).
tff(v_xa,type,
v_xa: $i ).
tff(t_c,type,
t_c: $i ).
tff(c_Fun_Ofcomp,type,
c_Fun_Ofcomp: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_Com_Ocom_OAss,type,
c_Com_Ocom_OAss: ( $i * $i ) > $i ).
tff(v_f,type,
v_f: $i ).
tff(c_Fun_Ocomp,type,
c_Fun_Ocomp: ( $i * $i * $i * $i * $i ) > $i ).
tff(class_Lattices_Obounded__lattice,type,
class_Lattices_Obounded__lattice: $i > $o ).
tff(c_Option_Othe,type,
c_Option_Othe: $i > $i ).
tff(class_Lattices_Olattice,type,
class_Lattices_Olattice: $i > $o ).
tff(c_Option_Ooption_OSome,type,
c_Option_Ooption_OSome: ( $i * $i ) > $i ).
tff(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1,type,
c_Natural_Osko__Natural__Xevaln__elim__cases__6__1: ( $i * $i * $i * $i ) > $i ).
tff(c_Com_Ocom_OCond,type,
c_Com_Ocom_OCond: ( $i * $i * $i ) > $i ).
tff(c_Com_Ocom_OWhile,type,
c_Com_Ocom_OWhile: ( $i * $i ) > $i ).
tff(c_Fun_Oid,type,
c_Fun_Oid: $i > $i ).
tff(t_a,type,
t_a: $i ).
tff(class_OrderedGroup_Olordered__ab__group__add,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(c_Com_Ocom_Ocom__case,type,
c_Com_Ocom_Ocom__case: ( $i * $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
tff(class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
tff(c_COMBB,type,
c_COMBB: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_Fun_Oinj__on,type,
c_Fun_Oinj__on: ( $i * $i * $i * $i ) > $o ).
tff(c_Orderings_Obot__class_Obot,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(c_Lattices_Oupper__semilattice__class_Osup,type,
c_Lattices_Oupper__semilattice__class_Osup: ( $i * $i * $i ) > $i ).
tff(c_Set_Ovimage,type,
c_Set_Ovimage: ( $i * $i * $i * $i ) > $i ).
tff(tc_Option_Ooption,type,
tc_Option_Ooption: $i > $i ).
tff(c_Hoare__Mirabelle_Otriple_Otriple__rec,type,
c_Hoare__Mirabelle_Otriple_Otriple__rec: ( $i * $i * $i * $i ) > $i ).
tff(v_pn,type,
v_pn: $i ).
tff(c_Com_Ocom_OCall,type,
c_Com_Ocom_OCall: ( $i * $i * $i ) > $i ).
tff(c_Com_Ocom_OLocal,type,
c_Com_Ocom_OLocal: ( $i * $i * $i ) > $i ).
tff(c_Com_Ocom_OSKIP,type,
c_Com_Ocom_OSKIP: $i ).
tff(tc_Com_Ocom,type,
tc_Com_Ocom: $i ).
tff(class_Orderings_Otop,type,
class_Orderings_Otop: $i > $o ).
tff(c_Suc,type,
c_Suc: $i > $i ).
tff(c_Natural_Oevalc,type,
c_Natural_Oevalc: $i ).
tff(c_lessequals,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(tc_nat,type,
tc_nat: $i ).
tff(v_g,type,
v_g: $i ).
tff(c_Hoare__Mirabelle_Otriple_Otriple__case,type,
c_Hoare__Mirabelle_Otriple_Otriple__case: ( $i * $i * $i * $i ) > $i ).
tff(tc_fun,type,
tc_fun: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Oidom,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(c_Hoare__Mirabelle_Ohoare__derivs,type,
c_Hoare__Mirabelle_Ohoare__derivs: ( $i * $i * $i ) > $o ).
tff(tc_bool,type,
tc_bool: $i ).
tff(c_Hoare__Mirabelle_Otriple__valid,type,
c_Hoare__Mirabelle_Otriple__valid: ( $i * $i * $i ) > $o ).
tff(tc_Com_Opname,type,
tc_Com_Opname: $i ).
tff(class_Lattices_Oupper__semilattice,type,
class_Lattices_Oupper__semilattice: $i > $o ).
tff(c_HOL_Ozero__class_Ozero,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(class_HOL_Oord,type,
class_HOL_Oord: $i > $o ).
tff(c_in,type,
c_in: $i > $i ).
tff(c_Com_OWT,type,
c_Com_OWT: $i > $o ).
tff(class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(hAPP,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Hoare__Mirabelle_Otriple_Otriple,type,
c_Hoare__Mirabelle_Otriple_Otriple: $i > $i ).
tff(c_Com_Ocom_Ocom__rec,type,
c_Com_Ocom_Ocom__rec: ( $i * $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(c_Hoare__Mirabelle_Ohoare__valids,type,
c_Hoare__Mirabelle_Ohoare__valids: ( $i * $i * $i ) > $o ).
tff(class_OrderedGroup_Ogroup__add,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(hBOOL,type,
hBOOL: $i > $o ).
tff(v_Procs,type,
v_Procs: $i ).
tff(c_Com_Ocom_OSemi,type,
c_Com_Ocom_OSemi: ( $i * $i ) > $i ).
tff(c_HOL_Ominus__class_Ominus,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(class_Orderings_Obot,type,
class_Orderings_Obot: $i > $o ).
tff(class_OrderedGroup_Opordered__ab__group__add,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(t_b,type,
t_b: $i ).
tff(c_Hoare__Mirabelle_OMGT,type,
c_Hoare__Mirabelle_OMGT: $i > $i ).
tff(c_Set_Oimage,type,
c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).
tff(tc_Hoare__Mirabelle_Otriple,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
tff(c_Com_Obody,type,
c_Com_Obody: $i ).
tff(c_Natural_Oevaln,type,
c_Natural_Oevaln: ( $i * $i * $i * $i ) > $o ).
tff(c_COMBS,type,
c_COMBS: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_Option_Ooption_ONone,type,
c_Option_Ooption_ONone: $i > $i ).
tff(c_Com_Ocom_OBODY,type,
c_Com_Ocom_OBODY: $i ).
tff(f_2218,axiom,
~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,v_pn)),v_x),v_xa)),
file(unknown,unknown) ).
tff(f_2216,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_x),v_xa)),
file(unknown,unknown) ).
tff(f_2090,axiom,
! [V_pn,V_s0,V_s1] :
( hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),V_s1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_s1)) ),
file(unknown,unknown) ).
tff(c_924,plain,
~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,v_pn)),v_x),v_xa)),
inference(cnfTransformation,[status(thm)],[f_2218]) ).
tff(c_922,plain,
hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),v_x),v_xa)),
inference(cnfTransformation,[status(thm)],[f_2216]) ).
tff(c_65354,plain,
! [V_pn_3681,V_s0_3682,V_s1_3683] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_3681))),V_s0_3682),V_s1_3683))
| hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,V_pn_3681)),V_s0_3682),V_s1_3683)) ),
inference(cnfTransformation,[status(thm)],[f_2090]) ).
tff(c_65395,plain,
hBOOL(hAPP(hAPP(hAPP(c_Natural_Oevalc,hAPP(c_Com_Ocom_OBODY,v_pn)),v_x),v_xa)),
inference(resolution,[status(thm)],[c_922,c_65354]) ).
tff(c_65401,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_924,c_65395]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV897-1 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Apr 9 04:54:37 EDT 2025
% 0.13/0.34 % CPUTime :
% 27.91/11.81 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.91/11.81
% 27.91/11.81 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------