%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWV901-1 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n005.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 273.96s 217.66s
% Output : CNFRefutation 274.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of formulae : 38 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 60 ( 16 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 50 ( 28 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 35 ( 33 usr; 3 prp; 0-9 aty)
% Number of functors : 61 ( 61 usr; 11 con; 0-6 aty)
% Number of variables : 56 ( 56 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_Complete__Lattice_Ocomplete__lattice > c_Map_Omap__le > c_Fun_Oinj__on > c_lessequals > c_in > c_Hoare__Mirabelle_Ohoare__valids > c_Hoare__Mirabelle_Ohoare__derivs > c_HOL_Oord__class_Oless > c_OrderedGroup_Oab__semigroup__mult > c_Finite__Set_Ofinite > hBOOL > class_Ring__and__Field_Oordered__idom > 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_Olower__semilattice > class_Lattices_Olattice > class_Lattices_Odistrib__lattice > class_Lattices_Obounded__lattice > class_Lattices_Oboolean__algebra > class_HOL_Oord > class_Finite__Set_Ofinite_Ofinite > class_Complete__Lattice_Ocomplete__lattice > c_Com_OWT > c_COMBC > c_COMBB > c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1 > c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1 > c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1 > c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1 > c_Set_Ovimage > c_Set_Oimage > c_Map_Osko__Map__XdomD__1__1 > c_Map_Omap__add > c_Hoare__Mirabelle_Otriple_Otriple > c_Complete__Lattice_Ocomplete__lattice__class_OSUPR > c_Set_Oinsert > c_SetInterval_Oord__class_OatLeastAtMost > c_Map_Oran > c_Map_Omap__of > c_Map_Odom > c_Lattices_Oupper__semilattice__class_Osup > c_HOL_Ominus__class_Ominus > c_Finite__Set_Ofold1Set > c_Finite__Set_Ofold1 > c_COMBK > c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2 > c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1 > tc_fun > hAPP > c_The > c_Set_Ocontents > c_Option_Oset > c_Option_Ooption_OSome > c_Nitpick_Osko__Nitpick__XEx1__def__1__3 > c_Inductive_Ocomplete__lattice__class_Ogfp > c_HOL_Ouminus__class_Ouminus > c_Finite__Set_Olinorder__class_OMin > c_Finite__Set_Olinorder__class_OMax > c_Finite__Set_Ocard > c_Complete__Lattice_OSup__class_OSup > c_Complete__Lattice_OInf__class_OInf > c_Collect > #nlpp > v_sko__Hoare__Mirabelle__XMGF__lemma1__1 > tc_Option_Ooption > tc_Hoare__Mirabelle_Otriple > c_fequal > c_Orderings_Otop__class_Otop > c_Orderings_Obot__class_Obot > c_Option_Othe > c_Option_Ooption_ONone > c_Natural_Oevalc > c_Lattices_Olower__semilattice__class_Oinf > c_Com_Osko__Com__XWTs__elim__cases__7__1 > v_y > v_pn > v_Fa > tc_nat > tc_bool > tc_Com_Ostate > tc_Com_Opname > tc_Com_Ocom > c_Hoare__Mirabelle_Ostate__not__singleton > c_Hoare__Mirabelle_OMGT > c_Com_Ocom_OBODY > c_Com_Obody > c_Com_OWT__bodies
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(tc_Com_Ostate,type,
tc_Com_Ostate: $i ).
tff(c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1,type,
c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_Hoare__Mirabelle_OMGT,type,
c_Hoare__Mirabelle_OMGT: $i ).
tff(c_Set_Oinsert,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
tff(c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1,type,
c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_COMBK,type,
c_COMBK: ( $i * $i * $i ) > $i ).
tff(c_Map_Osko__Map__XdomD__1__1,type,
c_Map_Osko__Map__XdomD__1__1: ( $i * $i * $i * $i ) > $i ).
tff(c_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(c_Option_Oset,type,
c_Option_Oset: ( $i * $i ) > $i ).
tff(c_Orderings_Otop__class_Otop,type,
c_Orderings_Otop__class_Otop: $i > $i ).
tff(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1,type,
c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1: ( $i * $i * $i ) > $i ).
tff(c_fequal,type,
c_fequal: $i > $i ).
tff(c_Finite__Set_Ofold1Set,type,
c_Finite__Set_Ofold1Set: ( $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1,type,
c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(class_Lattices_Obounded__lattice,type,
class_Lattices_Obounded__lattice: $i > $o ).
tff(c_Finite__Set_Ofold1,type,
c_Finite__Set_Ofold1: ( $i * $i * $i ) > $i ).
tff(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2,type,
c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2: ( $i * $i * $i ) > $i ).
tff(c_Option_Othe,type,
c_Option_Othe: $i > $i ).
tff(class_Lattices_Olattice,type,
class_Lattices_Olattice: $i > $o ).
tff(v_y,type,
v_y: $i ).
tff(c_Option_Ooption_OSome,type,
c_Option_Ooption_OSome: ( $i * $i ) > $i ).
tff(c_Finite__Set_Olinorder__class_OMin,type,
c_Finite__Set_Olinorder__class_OMin: ( $i * $i ) > $i ).
tff(c_Finite__Set_Olinorder__class_OMax,type,
c_Finite__Set_Olinorder__class_OMax: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Olordered__ab__group__add,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
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_Map_Omap__of,type,
c_Map_Omap__of: ( $i * $i * $i ) > $i ).
tff(c_Fun_Oinj__on,type,
c_Fun_Oinj__on: ( $i * $i * $i * $i ) > $o ).
tff(c_OrderedGroup_Oab__semigroup__mult,type,
c_OrderedGroup_Oab__semigroup__mult: ( $i * $i ) > $o ).
tff(c_Complete__Lattice_OInf__class_OInf,type,
c_Complete__Lattice_OInf__class_OInf: ( $i * $i ) > $i ).
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(v_pn,type,
v_pn: $i ).
tff(c_Hoare__Mirabelle_Otriple_Otriple,type,
c_Hoare__Mirabelle_Otriple_Otriple: ( $i * $i * $i * $i ) > $i ).
tff(c_Lattices_Olower__semilattice__class_Oinf,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i ).
tff(c_Collect,type,
c_Collect: ( $i * $i ) > $i ).
tff(class_Lattices_Oboolean__algebra,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(c_Map_Omap__add,type,
c_Map_Omap__add: ( $i * $i * $i * $i ) > $i ).
tff(c_Com_OWT__bodies,type,
c_Com_OWT__bodies: $o ).
tff(c_Inductive_Ocomplete__lattice__class_Ogfp,type,
c_Inductive_Ocomplete__lattice__class_Ogfp: ( $i * $i ) > $i ).
tff(v_Fa,type,
v_Fa: $i ).
tff(c_Map_Oran,type,
c_Map_Oran: ( $i * $i * $i ) > $i ).
tff(c_Hoare__Mirabelle_Ostate__not__singleton,type,
c_Hoare__Mirabelle_Ostate__not__singleton: $o ).
tff(tc_Com_Ocom,type,
tc_Com_Ocom: $i ).
tff(class_Orderings_Otop,type,
class_Orderings_Otop: $i > $o ).
tff(v_sko__Hoare__Mirabelle__XMGF__lemma1__1,type,
v_sko__Hoare__Mirabelle__XMGF__lemma1__1: $i > $i ).
tff(class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(c_lessequals,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: ( $i * $i * $i * $i ) > $i ).
tff(c_in,type,
c_in: ( $i * $i * $i ) > $o ).
tff(c_COMBC,type,
c_COMBC: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(tc_nat,type,
tc_nat: $i ).
tff(c_Finite__Set_Ocard,type,
c_Finite__Set_Ocard: ( $i * $i ) > $i ).
tff(tc_fun,type,
tc_fun: ( $i * $i ) > $i ).
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_Map_Odom,type,
c_Map_Odom: ( $i * $i * $i ) > $i ).
tff(tc_Com_Opname,type,
tc_Com_Opname: $i ).
tff(class_Lattices_Oupper__semilattice,type,
class_Lattices_Oupper__semilattice: $i > $o ).
tff(class_HOL_Oord,type,
class_HOL_Oord: $i > $o ).
tff(c_Complete__Lattice_Ocomplete__lattice,type,
c_Complete__Lattice_Ocomplete__lattice: ( $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $o ).
tff(c_Complete__Lattice_OSup__class_OSup,type,
c_Complete__Lattice_OSup__class_OSup: ( $i * $i ) > $i ).
tff(c_Natural_Oevalc,type,
c_Natural_Oevalc: $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(c_Map_Omap__le,type,
c_Map_Omap__le: ( $i * $i * $i * $i ) > $o ).
tff(hAPP,type,
hAPP: ( $i * $i ) > $i ).
tff(class_Finite__Set_Ofinite_Ofinite,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
tff(class_Lattices_Odistrib__lattice,type,
class_Lattices_Odistrib__lattice: $i > $o ).
tff(c_Finite__Set_Ofinite,type,
c_Finite__Set_Ofinite: ( $i * $i ) > $o ).
tff(c_Hoare__Mirabelle_Ohoare__valids,type,
c_Hoare__Mirabelle_Ohoare__valids: ( $i * $i * $i ) > $o ).
tff(c_HOL_Ouminus__class_Ouminus,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Ogroup__add,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(hBOOL,type,
hBOOL: $i > $o ).
tff(c_Nitpick_Osko__Nitpick__XEx1__def__1__3,type,
c_Nitpick_Osko__Nitpick__XEx1__def__1__3: ( $i * $i ) > $i ).
tff(class_Lattices_Olower__semilattice,type,
class_Lattices_Olower__semilattice: $i > $o ).
tff(c_HOL_Ominus__class_Ominus,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(c_Com_Osko__Com__XWTs__elim__cases__7__1,type,
c_Com_Osko__Com__XWTs__elim__cases__7__1: $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(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1,type,
c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1: ( $i * $i * $i * $i * $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_The,type,
c_The: ( $i * $i ) > $i ).
tff(class_Complete__Lattice_Ocomplete__lattice,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
tff(c_SetInterval_Oord__class_OatLeastAtMost,type,
c_SetInterval_Oord__class_OatLeastAtMost: ( $i * $i * $i ) > $i ).
tff(c_Set_Ocontents,type,
c_Set_Ocontents: ( $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_3981,axiom,
hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_OSome(v_y,tc_Com_Ocom),
file(unknown,unknown) ).
tff(f_3976,axiom,
c_Com_OWT__bodies,
file(unknown,unknown) ).
tff(f_3380,axiom,
! [V_pn,V_b] :
( ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_OSome(V_b,tc_Com_Ocom) )
| ~ c_Com_OWT__bodies
| c_Com_OWT(V_b) ),
file(unknown,unknown) ).
tff(f_3781,axiom,
! [T_a,V_A] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),V_A,tc_fun(T_a,tc_bool)),
file(unknown,unknown) ).
tff(f_3267,axiom,
! [V_x,T_a] : ( c_Option_Oset(c_Option_Ooption_OSome(V_x,T_a),T_a) = c_Set_Oinsert(V_x,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ),
file(unknown,unknown) ).
tff(f_2941,axiom,
! [T_a,V_a] : ( c_Collect(hAPP(c_fequal(T_a),V_a),T_a) = c_Set_Oinsert(V_a,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_bool)),T_a) ),
file(unknown,unknown) ).
tff(f_569,axiom,
! [V_P,T_a] : ( c_Collect(V_P,T_a) = V_P ),
file(unknown,unknown) ).
tff(f_3975,axiom,
c_Hoare__Mirabelle_Ostate__not__singleton,
file(unknown,unknown) ).
tff(f_3409,axiom,
! [V_c] :
( c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate)
| ~ c_Com_OWT(V_c)
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
file(unknown,unknown) ).
tff(f_3528,axiom,
! [V_G,V_ts,T_a,V_G_H] :
( c_Hoare__Mirabelle_Ohoare__derivs(V_G,V_ts,T_a)
| ~ c_lessequals(V_G_H,V_G,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_bool))
| ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_H,V_ts,T_a) ),
file(unknown,unknown) ).
tff(f_3596,axiom,
! [V_g,T_a,V_A,V_f,T_c,T_b] : ( c_Set_Oimage(V_f,c_Set_Oimage(V_g,V_A,T_c,T_b),T_b,T_a) = c_Set_Oimage(c_COMBB(V_f,V_g,T_b,T_a,T_c),V_A,T_c,T_a) ),
file(unknown,unknown) ).
tff(f_3984,axiom,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,v_y),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
file(unknown,unknown) ).
tff(c_1342,plain,
hAPP(c_Com_Obody,v_pn) = c_Option_Ooption_OSome(v_y,tc_Com_Ocom),
inference(cnfTransformation,[status(thm)],[f_3981]) ).
tff(c_1334,plain,
c_Com_OWT__bodies,
inference(cnfTransformation,[status(thm)],[f_3976]) ).
tff(c_1112,plain,
! [V_b_2059,V_pn_2058] :
( c_Com_OWT(V_b_2059)
| ~ c_Com_OWT__bodies
| ( hAPP(c_Com_Obody,V_pn_2058) != c_Option_Ooption_OSome(V_b_2059,tc_Com_Ocom) ) ),
inference(cnfTransformation,[status(thm)],[f_3380]) ).
tff(c_1653,plain,
! [V_b_2585,V_pn_2586] :
( c_Com_OWT(V_b_2585)
| ( hAPP(c_Com_Obody,V_pn_2586) != c_Option_Ooption_OSome(V_b_2585,tc_Com_Ocom) ) ),
inference(demodulation,[status(thm),theory(equality)],[c_1334,c_1112]) ).
tff(c_1654,plain,
! [V_b_2585] :
( c_Com_OWT(V_b_2585)
| ( c_Option_Ooption_OSome(v_y,tc_Com_Ocom) != c_Option_Ooption_OSome(V_b_2585,tc_Com_Ocom) ) ),
inference(superposition,[status(thm),theory(equality)],[c_1342,c_1653]) ).
tff(c_1252,plain,
! [T_a_2291,V_A_2292] : c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(T_a_2291,tc_bool)),V_A_2292,tc_fun(T_a_2291,tc_bool)),
inference(cnfTransformation,[status(thm)],[f_3781]) ).
tff(c_1084,plain,
! [V_x_2015,T_a_2016] : ( c_Set_Oinsert(V_x_2015,c_Orderings_Obot__class_Obot(tc_fun(T_a_2016,tc_bool)),T_a_2016) = c_Option_Oset(c_Option_Ooption_OSome(V_x_2015,T_a_2016),T_a_2016) ),
inference(cnfTransformation,[status(thm)],[f_3267]) ).
tff(c_980,plain,
! [V_a_1814,T_a_1813] : ( c_Set_Oinsert(V_a_1814,c_Orderings_Obot__class_Obot(tc_fun(T_a_1813,tc_bool)),T_a_1813) = c_Collect(hAPP(c_fequal(T_a_1813),V_a_1814),T_a_1813) ),
inference(cnfTransformation,[status(thm)],[f_2941]) ).
tff(c_7086,plain,
! [T_a_2953,V_a_2954] : ( c_Collect(hAPP(c_fequal(T_a_2953),V_a_2954),T_a_2953) = c_Option_Oset(c_Option_Ooption_OSome(V_a_2954,T_a_2953),T_a_2953) ),
inference(demodulation,[status(thm),theory(equality)],[c_1084,c_980]) ).
tff(c_216,plain,
! [V_P_382,T_a_383] : ( c_Collect(V_P_382,T_a_383) = V_P_382 ),
inference(cnfTransformation,[status(thm)],[f_569]) ).
tff(c_7092,plain,
! [T_a_2953,V_a_2954] : ( hAPP(c_fequal(T_a_2953),V_a_2954) = c_Option_Oset(c_Option_Ooption_OSome(V_a_2954,T_a_2953),T_a_2953) ),
inference(superposition,[status(thm),theory(equality)],[c_7086,c_216]) ).
tff(c_1332,plain,
c_Hoare__Mirabelle_Ostate__not__singleton,
inference(cnfTransformation,[status(thm)],[f_3975]) ).
tff(c_1120,plain,
! [V_c_2072] :
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| ~ c_Com_OWT__bodies
| ~ c_Com_OWT(V_c_2072)
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c_2072),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(cnfTransformation,[status(thm)],[f_3409]) ).
tff(c_1439,plain,
! [V_c_2072] :
( ~ c_Com_OWT(V_c_2072)
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,V_c_2072),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(demodulation,[status(thm),theory(equality)],[c_1334,c_1332,c_1120]) ).
tff(c_1456,plain,
! [V_c_2072] :
( ~ c_Com_OWT(V_c_2072)
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),c_Option_Oset(c_Option_Ooption_OSome(hAPP(c_Hoare__Mirabelle_OMGT,V_c_2072),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate) ),
inference(demodulation,[status(thm),theory(equality)],[c_1084,c_1439]) ).
tff(c_524764,plain,
! [V_c_164434] :
( ~ c_Com_OWT(V_c_164434)
| c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_c_164434)),tc_Com_Ostate) ),
inference(demodulation,[status(thm),theory(equality)],[c_7092,c_1456]) ).
tff(c_1160,plain,
! [V_G_H_2142,V_ts_2140,T_a_2141,V_G_2139] :
( ~ c_Hoare__Mirabelle_Ohoare__derivs(V_G_H_2142,V_ts_2140,T_a_2141)
| ~ c_lessequals(V_G_H_2142,V_G_2139,tc_fun(tc_Hoare__Mirabelle_Otriple(T_a_2141),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G_2139,V_ts_2140,T_a_2141) ),
inference(cnfTransformation,[status(thm)],[f_3528]) ).
tff(c_524768,plain,
! [V_G_2139,V_c_164434] :
( ~ c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),V_G_2139,tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool))
| c_Hoare__Mirabelle_Ohoare__derivs(V_G_2139,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_c_164434)),tc_Com_Ostate)
| ~ c_Com_OWT(V_c_164434) ),
inference(resolution,[status(thm)],[c_524764,c_1160]) ).
tff(c_887937,plain,
! [V_G_167225,V_c_167226] :
( c_Hoare__Mirabelle_Ohoare__derivs(V_G_167225,hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_c_167226)),tc_Com_Ostate)
| ~ c_Com_OWT(V_c_167226) ),
inference(demodulation,[status(thm),theory(equality)],[c_1252,c_524768]) ).
tff(c_1180,plain,
! [V_g_2175,T_c_2179,T_b_2180,V_A_2177,V_f_2178,T_a_2176] : ( c_Set_Oimage(c_COMBB(V_f_2178,V_g_2175,T_b_2180,T_a_2176,T_c_2179),V_A_2177,T_c_2179,T_a_2176) = c_Set_Oimage(V_f_2178,c_Set_Oimage(V_g_2175,V_A_2177,T_c_2179,T_b_2180),T_b_2180,T_a_2176) ),
inference(cnfTransformation,[status(thm)],[f_3596]) ).
tff(c_1346,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_COMBB(c_Hoare__Mirabelle_OMGT,c_Com_Ocom_OBODY,tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_Com_Opname),c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,v_y),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
inference(cnfTransformation,[status(thm)],[f_3984]) ).
tff(c_1433,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,v_y),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
inference(demodulation,[status(thm),theory(equality)],[c_1180,c_1346]) ).
tff(c_1453,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Option_Oset(c_Option_Ooption_OSome(hAPP(c_Hoare__Mirabelle_OMGT,v_y),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),tc_Com_Ostate),
inference(demodulation,[status(thm),theory(equality)],[c_1084,c_1433]) ).
tff(c_629084,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(c_Set_Oimage(c_Hoare__Mirabelle_OMGT,c_Set_Oimage(c_Com_Ocom_OBODY,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname,tc_Com_Ocom),tc_Com_Ocom,tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_fequal(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,v_y)),tc_Com_Ostate),
inference(demodulation,[status(thm),theory(equality)],[c_7092,c_1453]) ).
tff(c_887953,plain,
~ c_Com_OWT(v_y),
inference(resolution,[status(thm)],[c_887937,c_629084]) ).
tff(c_887962,plain,
$false,
inference(resolution,[status(thm)],[c_1654,c_887953]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV901-1 : TPTP v9.0.0. Released v4.1.0.
% 0.03/0.12 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34 % Computer : n005.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 04:55:12 EDT 2025
% 0.13/0.34 % CPUTime :
% 273.96/217.66 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 273.96/217.66
% 273.96/217.66 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------