TSTP Solution File: SWV902-1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWV902-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n026.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 Aug 31 21:48:34 EDT 2023
% Result : Unsatisfiable 0.90s 0.98s
% Output : CNFRefutation 0.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 107
% Syntax : Number of formulae : 119 ( 13 unt; 100 typ; 0 def)
% Number of atoms : 27 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 199 ( 85 >; 114 *; 0 +; 0 <<)
% Number of predicates : 36 ( 34 usr; 3 prp; 0-9 aty)
% Number of functors : 66 ( 66 usr; 13 con; 0-6 aty)
% Number of variables : 40 ( 2 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
tc_bool: $i ).
tff(decl_23,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_24,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_25,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i ).
tff(decl_26,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_27,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(decl_28,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(decl_29,type,
c_Lattices_Oupper__semilattice__class_Osup: ( $i * $i * $i ) > $i ).
tff(decl_30,type,
class_Lattices_Oupper__semilattice: $i > $o ).
tff(decl_31,type,
class_Lattices_Olattice: $i > $o ).
tff(decl_32,type,
class_Lattices_Olower__semilattice: $i > $o ).
tff(decl_33,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_34,type,
c_Orderings_Otop__class_Otop: $i > $i ).
tff(decl_35,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(decl_36,type,
c_Option_Ooption_ONone: $i > $i ).
tff(decl_37,type,
c_Option_Oset: ( $i * $i ) > $i ).
tff(decl_38,type,
c_Option_Ooption_OSome: ( $i * $i ) > $i ).
tff(decl_39,type,
c_Map_Omap__add: ( $i * $i * $i * $i ) > $i ).
tff(decl_40,type,
c_Set_Ovimage: ( $i * $i * $i * $i ) > $i ).
tff(decl_41,type,
c_Set_Oimage: ( $i * $i * $i * $i ) > $i ).
tff(decl_42,type,
c_Fun_Oinj__on: ( $i * $i * $i * $i ) > $o ).
tff(decl_43,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
tff(decl_44,type,
c_COMBK: ( $i * $i * $i ) > $i ).
tff(decl_45,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: ( $i * $i * $i * $i ) > $i ).
tff(decl_46,type,
c_Finite__Set_Ocard: ( $i * $i ) > $i ).
tff(decl_47,type,
c_Finite__Set_Ofinite: ( $i * $i ) > $o ).
tff(decl_48,type,
class_HOL_Ominus: $i > $o ).
tff(decl_49,type,
t_a: $i ).
tff(decl_50,type,
v_x: $i ).
tff(decl_51,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(decl_52,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_53,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(decl_54,type,
c_SetInterval_Oord__class_OatLeastAtMost: ( $i * $i * $i ) > $i ).
tff(decl_55,type,
c_OrderedGroup_Oab__semigroup__mult: ( $i * $i ) > $o ).
tff(decl_56,type,
c_Finite__Set_Ofold1: ( $i * $i * $i ) > $i ).
tff(decl_57,type,
c_in: ( $i * $i * $i ) > $i ).
tff(decl_58,type,
hBOOL: $i > $o ).
tff(decl_59,type,
c_Collect: ( $i * $i ) > $i ).
tff(decl_60,type,
c_Hoare__Mirabelle_OMGT: $i ).
tff(decl_61,type,
tc_Com_Ostate: $i ).
tff(decl_62,type,
c_Hoare__Mirabelle_Otriple_Otriple: $i > $i ).
tff(decl_63,type,
c_fequal: $i > $i ).
tff(decl_64,type,
c_Natural_Oevalc: $i > $i ).
tff(decl_65,type,
c_Map_Omap__le: ( $i * $i * $i * $i ) > $o ).
tff(decl_66,type,
c_Complete__Lattice_OSup__class_OSup: ( $i * $i ) > $i ).
tff(decl_67,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(decl_68,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(decl_69,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(decl_70,type,
c_COMBS: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_71,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_72,type,
class_Lattices_Odistrib__lattice: $i > $o ).
tff(decl_73,type,
c_Finite__Set_Ofold1Set: ( $i * $i * $i ) > $i ).
tff(decl_74,type,
c_The: ( $i * $i ) > $i ).
tff(decl_75,type,
c_Complete__Lattice_Ocomplete__lattice: ( $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_76,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(decl_77,type,
c_Complete__Lattice_OInf__class_OInf: ( $i * $i ) > $i ).
tff(decl_78,type,
class_Lattices_Obounded__lattice: $i > $o ).
tff(decl_79,type,
c_Map_Odom: ( $i * $i * $i ) > $i ).
tff(decl_80,type,
c_Hoare__Mirabelle_Ostate__not__singleton: $o ).
tff(decl_81,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_82,type,
class_Orderings_Otop: $i > $o ).
tff(decl_83,type,
c_Inductive_Ocomplete__lattice__class_Ogfp: ( $i * $i ) > $i ).
tff(decl_84,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(decl_85,type,
class_HOL_Ouminus: $i > $o ).
tff(decl_86,type,
c_Predicate_Oinv__imagep: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_87,type,
tc_Com_Ocom: $i ).
tff(decl_88,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
tff(decl_89,type,
tc_Com_Opname: $i ).
tff(decl_90,type,
c_COMBB: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_91,type,
c_Com_Ocom_OBODY: $i ).
tff(decl_92,type,
c_Hoare__Mirabelle_Ohoare__derivs: ( $i * $i * $i ) > $o ).
tff(decl_93,type,
c_Option_Othe: $i > $i ).
tff(decl_94,type,
c_Com_Obody: $i ).
tff(decl_95,type,
tc_Option_Ooption: $i > $i ).
tff(decl_96,type,
c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1: ( $i * $i * $i ) > $i ).
tff(decl_97,type,
c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2: ( $i * $i * $i ) > $i ).
tff(decl_98,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
tff(decl_99,type,
class_HOL_Oord: $i > $o ).
tff(decl_100,type,
c_Hoare__Mirabelle_Ohoare__valids: ( $i * $i * $i ) > $o ).
tff(decl_101,type,
c_Finite__Set_Olinorder__class_OMax: ( $i * $i ) > $i ).
tff(decl_102,type,
c_Nitpick_Osko__Nitpick__XEx1__def__1__3: ( $i * $i ) > $i ).
tff(decl_103,type,
c_Set_Ocontents: ( $i * $i ) > $i ).
tff(decl_104,type,
c_Finite__Set_Olinorder__class_OMin: ( $i * $i ) > $i ).
tff(decl_105,type,
c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_106,type,
c_Map_Oran: ( $i * $i * $i ) > $i ).
tff(decl_107,type,
c_Com_OWT: $i > $o ).
tff(decl_108,type,
v_sko__Hoare__Mirabelle__XMGF__lemma1__1: $i > $i ).
tff(decl_109,type,
c_Map_Omap__of: ( $i * $i * $i ) > $i ).
tff(decl_110,type,
v_y: $i ).
tff(decl_111,type,
c_Com_Osko__Com__XWTs__elim__cases__7__1: $i > $i ).
tff(decl_112,type,
c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_113,type,
c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_114,type,
c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_115,type,
c_Map_Osko__Map__XdomD__1__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_116,type,
c_Com_OWT__bodies: $o ).
tff(decl_117,type,
class_Orderings_Obot: $i > $o ).
tff(decl_118,type,
v_Fa: $i ).
tff(decl_119,type,
v_pn: $i ).
tff(decl_120,type,
tc_nat: $i ).
tff(decl_121,type,
c_COMBC: ( $i * $i * $i * $i * $i * $i ) > $i ).
cnf(cls_conjecture_7,negated_conjecture,
~ 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,hAPP(c_Com_Ocom_OBODY,v_x)),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('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_7) ).
cnf(cls_image__image_0,axiom,
c_Set_Oimage(X1,c_Set_Oimage(X2,X3,X4,X5),X5,X6) = c_Set_Oimage(c_COMBB(X1,X2,X5,X6,X4),X3,X4,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__image_0) ).
cnf(cls_asm_0,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ c_lessequals(X2,X1,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_asm_0) ).
cnf(cls_insert__subset_2,axiom,
( c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X4,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).
cnf(cls_empty__subsetI_0,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
cnf(cls_rev__image__eqI_0,axiom,
( hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
| ~ hBOOL(c_in(X1,X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
cnf(cls_conjecture_6,negated_conjecture,
hBOOL(c_in(v_x,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
cnf(c_0_7,negated_conjecture,
~ 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,hAPP(c_Com_Ocom_OBODY,v_x)),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),
cls_conjecture_7 ).
cnf(c_0_8,axiom,
c_Set_Oimage(X1,c_Set_Oimage(X2,X3,X4,X5),X5,X6) = c_Set_Oimage(c_COMBB(X1,X2,X5,X6,X4),X3,X4,X6),
cls_image__image_0 ).
cnf(c_0_9,negated_conjecture,
~ 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,hAPP(c_Com_Ocom_OBODY,v_x)),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(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,axiom,
( c_Hoare__Mirabelle_Ohoare__derivs(X1,X2,X3)
| ~ c_lessequals(X2,X1,tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_bool)) ),
cls_asm_0 ).
cnf(c_0_11,negated_conjecture,
~ c_lessequals(c_Set_Oinsert(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),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)),tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_bool)),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,axiom,
( c_lessequals(c_Set_Oinsert(X1,X2,X3),X4,tc_fun(X3,tc_bool))
| ~ c_lessequals(X2,X4,tc_fun(X3,tc_bool))
| ~ hBOOL(c_in(X1,X4,X3)) ),
cls_insert__subset_2 ).
cnf(c_0_13,axiom,
c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_bool)),X2,tc_fun(X1,tc_bool)),
cls_empty__subsetI_0 ).
cnf(c_0_14,negated_conjecture,
~ hBOOL(c_in(hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_x)),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)),tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).
cnf(c_0_15,axiom,
( hBOOL(c_in(hAPP(X4,X1),c_Set_Oimage(X4,X2,X3,X5),X5))
| ~ hBOOL(c_in(X1,X2,X3)) ),
cls_rev__image__eqI_0 ).
cnf(c_0_16,negated_conjecture,
~ hBOOL(c_in(hAPP(c_Com_Ocom_OBODY,v_x),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)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,negated_conjecture,
hBOOL(c_in(v_x,c_Map_Odom(c_Com_Obody,tc_Com_Opname,tc_Com_Ocom),tc_Com_Opname)),
cls_conjecture_6 ).
cnf(c_0_18,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_15]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWV902-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 29 11:03:20 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.59 start to proof: theBenchmark
% 0.90/0.98 % Version : CSE_E---1.5
% 0.90/0.98 % Problem : theBenchmark.p
% 0.90/0.98 % Proof found
% 0.90/0.98 % SZS status Theorem for theBenchmark.p
% 0.90/0.98 % SZS output start Proof
% See solution above
% 0.90/0.99 % Total time : 0.364000 s
% 0.90/0.99 % SZS output end Proof
% 0.90/0.99 % Total time : 0.386000 s
%------------------------------------------------------------------------------